DSpace Repository :: Browsing by Author "Mancilla-Aguilar, J. L."

Browsing by Author "Mancilla-Aguilar, J. L."

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A characterization of iISS for time-varying impulsive systems
(2018-12) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"Most of the existing characterizations of the integral input-to-state stability (iISS) property are not suitable for time varying or switched (nonlinear) systems. Previous work by the authors has shown that in such cases where converse Lyapunov theorems for stability are not available, iISS-Lyapunov functions may not exist. In these cases, the iISS property can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). This paper shows that such a characterization remains valid for time-varying impulsive systems, under an appropriate condition on the number of impulse times on each finite time interval."
A characterization of Integral ISS for switched and time-varying systems
(2018-02) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This paper provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics."
A characterization of strong iISS for time-varying impulsive systems
(2019-09) Haimovich, Hernán; Mancilla-Aguilar, J. L.; Cardone, Paula
"For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stability are not available. In these cases, the integral input-to-state stability (iISS) property is not equivalent to the existence of an iISS-Lyapunov function but can still be characterized as the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded energy input-bounded state (UBEBS). For impulsive systems, asymptotic stability can be weak (when the asymptotic decay depends only on elapsed time) or strong (when such a decay depends also on the number of impulses that occurred). This paper shows that the mentioned characterization of iISS remains valid for time-varying impulsive systems, provided that stability is understood in the strong sense. "
Converging-input convergent-state and related properties of time-varying impulsive systems
(2020-07-03) Mancilla-Aguilar, J. L.; Haimovich, Hernán
"Very recently, it has been shown that the standard notion of stability for impulsive systems, whereby the state is ensured to approach the equilibrium only as continuous time elapses, is too weak to allow for any meaningful type of robustness in a time-varying impulsive system setting. By strengthening the notion of stability so that convergence to the equilibrium occurs not only as time elapses but also as the number of jumps increases, some facts that are well-established for time-invariant nonimpulsive systems can be recovered for impulsive systems. In this context, our contribution is to provide novel results consisting in rather mild conditions under which stability under zero input implies stability under inputs that converge to zero in some appropriate sense."
Diseño de observadores en modos cuasi-deslizantes vía LMIs
(2008-07) Fraguío, Alberto Javier; Mancilla-Aguilar, J. L.; Zanini, Aníbal
"En este trabajo se presenta un observador robusto por modos cuasi-deslizantes para plantas con modelo nominal lineal e incertidumbres/pertubaciones de cierta clase particular. Las señales utilizadas para la estimación del vector de estados se suponen contaminadas con ruido del que sólo se conocen cotas. El diseño del observador se plantea como un problema de factibilidad LMI (Linear Matrix Inequalities) y se encuentran cotas para el error de estimación que pueden ser calculadas a priori. Posteriormente el diseño del observador se reformula como un problema de optimización GEVP (Generalized Eigen Value Problem) con el objeto de minimizar las cotas del error de estimación. El trabajo incluye un ejemplo numérico y simulaciones de un brazo robótico con un eje manejado por un motor de corriente continua."
An extension of LaSalle’s invariance principle for switched systems
(2006) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle’s Invariance Principle for these systems and state asymptotic stability criteria. We also present some related results that deal with the compactness of the trajectories of these switched systems and that are interesting by their own."
Global stability results for switched systems based on weak Lyapunov functions
(2017-06) Mancilla-Aguilar, J. L.; Haimovich, Hernán; García Galiñanes, Rafael
"In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbationlike one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-timevarying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm."
(Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization
(2021) Mancilla-Aguilar, J. L.; Haimovich, Hernán
"It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input."
Invariance results for constrained switched systems
(2010) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper we address invariance principles for nonlinear switched systems with otherwise arbitrary compact index set and with constrained switchings. We present an extension of LaSalle's invariance principle for these systems and derive by using detectability notions some convergence and asymptotic stability criteria. These results enable to take into account in the analysis of stability not only state-dependent constraints but also to treat the case in which the switching logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems."
ISS implies iISS even for switched and time-varying systems (if you are careful enough)
(2019-06) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function."
Nonrobustness of asymptotic stability of impulsive systems with inputs
(2020-12) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"Suitable continuity and boundedness assumptions on the function f defining the dynamics of a time-varying nonimpulsive system with inputs are known to make the system inherit stability properties from the zero-input system. Whether this type of robustness holds or not for impulsive systems was still an open question. By means of suitable (counter)examples, we show that such stability robustness with respect to the inclusion of inputs cannot hold in general, not even for impulsive systems with time-invariant flow and jump maps. In particular, we show that zero-input global uniform asymptotic stability (0-GUAS) does not imply converging input converging state (CICS), and that 0-GUAS and uniform bounded-energy input bounded state (UBEBS) do not imply integral input-to-state stability (iISS). We also comment on available existing results that, however, show that suitable constraints on the allowed impulse–time sequences indeed make some of these robustness properties possible."
On bounding a nonlinear system with a monotone positive system
(2017-12) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing this context in mind, we develop a novel componentwise bounding procedure applicable to both real and complex nonlinear systems with additive disturbances. A bound on the magnitude of the evolution of each state variable is obtained by computing a single trajectory of a well-specified 'bounding' system constructed from the original system equations and the available disturbance bounds. The bounding system is shown to have highly desirable properties, such as being monotone and positive. We provide preliminary results establishing that key stability features are preserved by the bounding system for systems in triangular form."
On zero-input stability inheritance for time-varying systems with decaying-to-zero input power
(2017-06) Mancilla-Aguilar, J. L.; Haimovich, Hernán
"Stability results for time-varying systems with inputs are relatively scarce, as opposed to the abundant literature available for time-invariant systems. This paper extends to time-varying systems existing results that ensure that if the input converges to zero in some specific sense, then the state trajectory will inherit stability properties from the corresponding zero-input system. This extension is non-trivial, in the sense that the proof technique is completely novel, and allows to recover the existing results under weaker assumptions in a unifying way."
Real time stable identification: A Nehari/SOS approach
(2007) García Galiñanes, Rafael; Sánchez-Peña, Ricardo; Mancilla-Aguilar, J. L.
"Here we present an adaptive identification algorithm based on Second Order section (SOS) model structures. The procedure guarantees stable transfer functions whenever the actual physical plant is stable, due to an optimal Nehari approximation step performed analytically. The procedure is suitable to be implemented in real time applications. Some examples illustrate the proposed algorithm."
Robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations
(2017-05) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper, it is shown that an algorithm for the stabilisation of switched systems introduced by the authors is robust with respect to perturbations which are unbounded in the supremum norm, but bounded in a power-like sense. The obtained stability results comprise, among others, both the exponential input-to-state stability and the exponential integral input-to-state stability properties of the closed-loop system and give a better description of the behaviour of the closed-loop system. "
Some invariance principles for constrained switched systems
(2010) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results may enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems."
Strong ISS implies strong iISS for time-varying impulsive systems
(2020-12) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems"
Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems
(2019-07) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim, the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state-dependent constraints, and the concept of weak zero-state detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-Time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of the switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semiquasi-Z-source inverter."
Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems
(2018) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of outputmaps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zerostate detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions, yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semi-quasi-Z-source inverter."
Uniform asymptotic stability of switched systems via detectability of reduced control systems
(2018-06) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper we present a criterion for the uniform global asymptotic stability of switched nonlinear systems with time/state-dependent switching constraints but with no dwell-time assumptions. This criterion is based on the existence of multiple weak common Lyapunov functions and on a detectability property of a reduced control system."

Browsing by Author "Mancilla-Aguilar, J. L."

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