Presentaciones a Congresos

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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."
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."
An alternative approach to the state observation problem for Lipschitz continuous systems with controls
(2010-07) Hernández, Santiago M.; García Galiñanes, Rafael
"In the present work we propose an alternative approach to the state observation problem for Lipschitz continuous systems with open-loop controls. We construct an observer based on a concept of observability weaker than that of the instantaneous observability. The resulting observation algorithm is then applicable under mild assumptions about the considered dynamical system".
On some goodness-of-fit tests and their connection to graphical methods with uncensored and censored data
(2019) Castro-Kuriss, Claudia; Huerta, Mauricio; Leiva, Víctor; Tapia, Alejandra
"In this work, we present goodness-of-fit tests related to the Kolmogorov-Smirnov and Michael statistics and connect them to graphical methods with uncensored and censored data. The Anderson-Darling test is often empirically more powerful than the Kolmogorov-Smirnov test. However, the former one cannot be related to graphical tools by means of probability plots, as the Kolmogorov-Smirnov test does. The Michael test is, in some cases, more powerful than the Anderson-Darling and Kolmogorov- Smirnov tests and can also be related to probability plots.We consider the Kolmogorov-Smirnov and Michael tests for detecting whether any distribution is suitable or not to model censored or uncensored data. We conduct numerical studies to show the performance of these tests and the corresponding graphical tools. Some comments related to big data and lifetime analysis, under the context of this study, are provided in the conclusions of this work."
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."
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."
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."
An extension of chaotic probability models to real-valued variables
(2008-07) Fierens, Pablo Ignacio
"Previous works have presented a frequentist interpretation of sets of measures as probabilistic models which have denominated chaotic models. Those models, however, dealt only with sets of probability measures on ﬁnite algebras, that is, probability measures which can be related to variables with a ﬁnite number of possible values. In this paper, an extension of chaotic models is proposed in order to deal with the more general case of real-valued variables."

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