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Your search keyword '"Gomez, Marco A."' showing total 30 results
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30 results on '"Gomez, Marco A."'

1. On the Notion of Safe Sliding Mode Control

Author

Gomez, Marco A., Cruz-Ancona, Christopher D., and Fridman, Leonid

Subjects
Electrical Engineering and Systems Science - Systems and Control
Abstract

Within the framework of Sliding Mode Control, safety critical control looks at two problems of theoretical significance: construct a sliding manifold that does not intersect a given unsafe set of the state space, and design a robust controller that safely takes the system trajectory to the manifold during the reaching phase and enforces the sliding motion. In this technical note, we address both problems. We introduce the notion of Safe Sliding Manifold (SSM) of relative degree one, and show that it is possible to construct it from the gradient of a class of Lyapunov-like energy functions, previously reported in the literature, used to asses stability and safety of a nominal system. The constructed SSM allows us providing a robust safe controller for a fair general class of uncertain nonlinear systems., Comment: 12 pages, 7 figures

Published
2022

2. Lyapunov stability tests for linear time-delay systems

Author

Mondié, Sabine, Egorov, Alexey, and Gomez, Marco A.

Subjects
Mathematics - Dynamical Systems, Electrical Engineering and Systems Science - Systems and Control, 34K20, I.1
Abstract

An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing research and potential extensions to other classes of delay systems are discussed., Comment: 19 pages, 4 figures, 1 table, journal paper submitted to Annual Reviews in Control

Published
2022

9. Closing the gap from nominal to robust asymptotic stabilization of time delay systems.

Author

Gomez, Marco A. and Cruz‐Ancona, Christopher D.

Subjects
*TIME delay systems, *SLIDING mode control, *FUNCTIONALS
Abstract

Summary: The control problem of a general class of perturbed linear invariant time‐delay systems within the Sliding Mode Control framework is addressed. We introduce a novel class of sliding manifolds with a structure not previously reported in the literature, which constructively emerges from complete type functionals of the corresponding nominal time‐delay systems and depends on the whole state of the system. A fundamental conclusion derived from this proposal is that every time‐delay system with matched perturbations, whose associated nominal system is exponentially stabilizable, is robustly asymptotically stabilizable. In fact, the introduced sliding manifold enables to construct discontinuous and continuous sliding mode control‐based algorithms that mitigate different classes of perturbations. [ABSTRACT FROM AUTHOR]

Published
2024
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12. Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo

Author

Mondié, Sabine and Gomez, Marco-Antonio

Subjects
Time-delay systems, Controller design, Sistemas con retardos, General Computer Science, Control and Systems Engineering, Stability analysis, Análisis de estabilidad, Linear systems, Sistemas lineales, Diseño de controladores
Abstract

[EN] Recent results on Lyapunov-Krasovskii functionals of complete type for linear time-delay systems are presented. The main concepts and results are introduced for the single delay system case, and necessary and sufficient stability conditions expressed in terms of the Lyapunov delay matrix are explained. The use of complete type functionals in analysis and controller design is discussed. The contribution focuses mainly at results of researchers in Mexico., [ES] Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio., Este trabajo ha sido realizado parcialmente gracias al apoyo del Conacyt, México, Proyecto A1-S-24796.

Published
2022

19. An improved finiteness test and a systematic procedure to compute the strong H2 norm of differential algebraic systems with multiple delays

Author

UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique, Gomez, Marco A., Michiels, Wim, Jungers, Raphaël M., Mattenet, Sébastien, De Iuliis, Vittorio, UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique, Gomez, Marco A., Michiels, Wim, Jungers, Raphaël M., Mattenet, Sébastien, and De Iuliis, Vittorio

Abstract

We study the strong H2 norm of systems modeled by semi-explicit Delay Differential Algebraic Equations (DDAEs). We recall that the finiteness of the strong H2 norm is linked to an algebraic decision problem that can be solved by checking a finite numbers of equalities. We first improve the verification of the finiteness condition. In particular, the complexity of our new condition removes a dependency on the number of delays. We also show that, without imposing further conditions on the system, the number of checks cannot be further reduced. The methodology relies on interpreting the verification of the finiteness conditions in terms of a Polynomial Identity Testing problem. Second we show, in a constructive way, that if the strong H2 norm is finite, the system can always be transformed into a regular neutral-type system with the same H2 norm, without derivatives in the input or in the output equations. This result closes a gap in the literature as such a transformation was known to exist only under additional assumptions on the system. The transformation enables the computation of the strong H2 norm using delay Lyapunov matrices. Illustrative examples are provided throughout the paper.

Published
2022

20. An improved finiteness test and a systematic procedure to compute the strong H2 norm of differential algebraic systems with multiple delays

Author

Gomez, Marco A., Michiels, Wim, Jungers, Raphaël M., Mattenet, Sébastien, De Iuliis, Vittorio, and UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique

Subjects
H2 norm, Differencial algebraic equation, system with time delay, QA
Abstract

We study the strong H2 norm of systems modeled by semi-explicit Delay Differential Algebraic Equations (DDAEs). We recall that the finiteness of the strong H2 norm is linked to an algebraic decision problem that can be solved by checking a finite numbers of equalities. We first improve the verification of the finiteness condition. In particular, the complexity of our new condition removes a dependency on the number of delays. We also show that, without imposing further conditions on the system, the number of checks cannot be further reduced. The methodology relies on interpreting the verification of the finiteness conditions in terms of a Polynomial Identity Testing problem. Second we show, in a constructive way, that if the strong H2 norm is finite, the system can always be transformed into a regular neutral-type system with the same H2 norm, without derivatives in the input or in the output equations. This result closes a gap in the literature as such a transformation was known to exist only under additional assumptions on the system. The transformation enables the computation of the strong H2 norm using delay Lyapunov matrices. Illustrative examples are provided throughout the paper.

Published
2022

21. Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo

Author

Mondié, Sabine|||0000-0002-0968-1899 and Gomez, Marco-Antonio|||0000-0002-5679-954X

Subjects
Time-delay systems, Controller design, Sistemas con retardos, Stability analysis, Análisis de estabilidad, Linear systems, Sistemas lineales, Diseño de controladores
Abstract

[EN] Recent results on Lyapunov-Krasovskii functionals of complete type for linear time-delay systems are presented. The main concepts and results are introduced for the single delay system case, and necessary and sufficient stability conditions expressed in terms of the Lyapunov delay matrix are explained. The use of complete type functionals in analysis and controller design is discussed. The contribution focuses mainly at results of researchers in Mexico. [ES] Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio. Este trabajo ha sido realizado parcialmente gracias al apoyo del Conacyt, México, Proyecto A1-S-24796.

Published
2022

28. Stabilisation of distributed time-delay systems: a smoothed spectral abscissa optimisation approach.

Author

Vite, Leopoldo, Gomez, Marco A., Mondié, Sabine, and Michiels, Wim

Subjects
*DISTRIBUTED parameter systems, *MATHEMATICAL optimization, *LINEAR systems, *NONLINEAR oscillators, *PROBLEM solving
Abstract

We address the stabilisation problem of linear time-invariant systems with pointwise and distributed delays. We first introduce the concept of the smoothed spectral abscissa, a robust stability measure previously studied for pointwise delay systems. We show that the new stability measure for distributed systems is smooth with respect to the system parameters, and robust in the sense that it provides a trade-off between the decay rate of the solution and the H 2 norm of the system. Next, we reformulate the stabilisation problem as an unconstrained minimisation problem considering the smoothed spectral abscissa as the objective function, and show that its properties enable solving the stabilisation problem by using standard gradient-based optimisation techniques. We show the potential of the proposed approach by using it for the stabilisation of a fleet of vehicles, and an oscillator with a class of time-varying delays in the input. [ABSTRACT FROM AUTHOR]

Published
2022
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29. A Scalable Approach for Consensus Stability Analysis of a Large-Scale Multiagent System With Single Delay

Author

Gomez, Marco A. and Ramirez, Adrian

Abstract

This note presents a scalable approach for consensus stability analysis of a general class of large-scale multiagent system (MAS) with single delay considering directed and undirected graphs. It is shown that, under certain conditions satisfied by several protocols reported in the literature, consensus in MAS can be ensured by studying a set comprising a small number of quasipolynomials of reduced complexity. Specifically, if the graph is undirected, it suffices to guarantee the stability of only two quasipolynomials in the set. If the graph is directed, then the set consists of a family of quasipolynomials, possibly two as well, associated with a polytope enclosing the eigenvalues of a Laplacian-like matrix. The approach renders the number of agents in the network irrelevant for consensus stability analysis, as illustrated using two consensus protocols as benchmark.

Published
2023
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30. Critical parameters for a class of integral difference equations.

Author

Ochoa‐Ortega, Gilberto and Gomez, Marco A.

Subjects
*DIFFERENCE equations, *INTEGRAL equations, *CLASS differences, *DIFFERENTIAL operators, *DELAY differential equations
Abstract

This contribution addresses the problem of calculating the critical parameters of a class of integral delay systems. The starting point of the analysis is a neutral‐type system with distributed delay that results from the application of a differential operator, and whose spectrum contains the spectrum of the integral system. Based on recent results concerning the delay Lyapunov matrix for the class of obtained neutral‐type systems, it is shown that the set of critical frequencies of the integral delay system is contained in the set of critical frequencies of a delay‐free system of matrix equations. [ABSTRACT FROM AUTHOR]

Published
2022
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