Artículos de publicaciones periódicas

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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."
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 results for switched homogeneous systems
(2016) Mancilla Aguilar, Jose Luis; García Galiñanes, Rafael
"In this paper, we prove the equivalence of weak attractivity, attractivity, global uniform asymptotic stability and exponential stability of switched homogeneous systems whose switching signals verify a certain property P. In addition we show that these stability properties imply that the system stability is robust with respect to disturbances in a power-like sense, which comprises both, the exponential ISS and iISS."
A state estimation strategy for a nonlinear switched system with unknown switching signals
(2021) Benítez, Oscar; García Galiñanes, Rafael
"A strategy is presented to estimate the state of a nonlinear autonomous switched system, with no knowledge of the switching signal, except its dwell time. To do so, algorithms to estimate the switching times and the current mode of the system are developed. The estimation of the switching times is based on approximating the second ( generalised) derivative of the output of the system via a convolution of this signal with a suitable function and on detecting the corresponding spikes. To estimate the modes, a scheme based on the use of a bank of observers (one for each mode) and of a bank of subsystems (for each step of the estimation process a suitable subset of the subsystems of the switched system) is developed. The algorithms run regardless of the state observer model, as long as its output error norm decays exponentially with a controlled decay rate."
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 stability properties of switched systems with switchings governed by digraphs
(2005-05) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael; Sontag, E.; Wang, Y.
"Characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph, are developed. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions."

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