Artículos de publicaciones periódicas

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Characterization of integral input-to-state stability for nonlinear time-varyng systems of infinite dimension
(2022) Mancilla Aguilar, Jose Luis; Rojas Ruiz, Jose; Haimovich, Hernan
For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded-energy input/bounded state (UBEBS) is established under a reasonable assumption of continuity of the trajectories with respect to the input, at the zero input. By particularizing to specific instances of infinite-dimensional systems, such as time-delay, or semilinear over Banach spaces, sufficient conditions are given in terms of the functions defining the dynamics. In addition, it is also shown that for semilinear systems whose nonlinear term satisfies an affine-in-the-state norm bound, it holds that iISS becomes equivalent to just 0-GUAS, a fact known to hold for bilinear systems. An additional important aspect is that the iISS notion considered is more general than the standard one.
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."
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."
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."
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."
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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