This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with ti... more This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with time-varying state and input delays. An integral sliding surface is firstly constructed. Then, by using the Lyapunov-Krasovskii functional and some specified matrices, a sufficient condition is obtained in the form of linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be asymptotically stable. Furthermore, a sliding mode controller law is synthesized to guarantee that the system trajectories can be driven onto the specified sliding surface in a finite time and maintained there for all subsequent time. Finally, an inverted pendulum model is used to illustrate the advantages and effectiveness of the design method.
... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertai... more ... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertainty was extensively studied in the literature where it is referred as norm bounded uncertainty (Khargonekar, Petersen, & Zhou, 1990). ...
ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed c... more ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H2H2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an LMILMI as a constraint.
This note proposes a systematic approach for the static output feedback control design for discre... more This note proposes a systematic approach for the static output feedback control design for discrete time linear systems. It is shown that if the open loop system satisfies some particular structural conditions, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the stronger
This chapter presents the different aspects of the design methodology that has been used to cope ... more This chapter presents the different aspects of the design methodology that has been used to cope with the RCAM design problem. A quadratic approach involving robust pole placement in a disk and the solution of parameter-dependent Riccati equations is proposed. Robustness as well as performance is accounted for by robust disk pole location that ensures robust stability and provides a good transient behaviour together with a specific selection of the weighting matrices involved in the Riccati equations.
Application de la commande robuste sequencee au controle de la transition operationnelle d’un sys... more Application de la commande robuste sequencee au controle de la transition operationnelle d’un systeme non lineaire Yann LABIT1, Pedro TEPPA1;2, Jacques BERNUSSOU1, Germain GARCIA1 1 Laboratoire d’Analyse et d’Architecture des Systemes du CNRS 7 Avenue du Colonel Roche, 31077 Toulouse, France 2 Universite Simon Bolivar, Valle de Sartenejas, Baruta, Caracas-Venezuelafylabit, pteppa, bernusoug@laas.fr Resume— Nous proposons, dans cet article, une approche systematique pour assurer la transition en stabilite d’un systeme dynamique non lineaire entre deux points operationnels. Ceci est realise dans un cadre d’un sequen- cement de lois de commande robuste issues de la satisfaction de contraintes en stabilite et en prenant compte de certaines specifications de perfor- mances locales qui restent valables dans un voisinage d’attraction d’un en- semble de points d’equilibre. L’approche proposee est implantee par l’in- termediaire de deux techniques : la premiere repose sur les fonctions cano- niques lineaires par morceaux tandis que la deuxieme se centralise sur des outils geometriques tels que les ellipsoi�
In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems... more In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems by dynamic output feedback is addressed. Using a time-scale decomposition. two smaller-order ε-independent quadratic stabilizability subproblems are solved and it is shown that when ε is sufficiently small the combination of the corresponding results yields a quadratic stabilizing controller for the full order uncertain system, the controller being singularly perturbed itself with the same parameter ε as that of the system.
This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with ti... more This paper proposes an integral sliding mode control (ISMC) for a class of linear systems with time-varying state and input delays. An integral sliding surface is firstly constructed. Then, by using the Lyapunov-Krasovskii functional and some specified matrices, a sufficient condition is obtained in the form of linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be asymptotically stable. Furthermore, a sliding mode controller law is synthesized to guarantee that the system trajectories can be driven onto the specified sliding surface in a finite time and maintained there for all subsequent time. Finally, an inverted pendulum model is used to illustrate the advantages and effectiveness of the design method.
... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertai... more ... matrices. is the uncertainty matrix which belongs to the following set: This kind of uncertainty was extensively studied in the literature where it is referred as norm bounded uncertainty (Khargonekar, Petersen, & Zhou, 1990). ...
ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed c... more ABSTRACT In this paper, the problem of robust pole assignment in a disk with an H2H2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H2H2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an LMILMI as a constraint.
This note proposes a systematic approach for the static output feedback control design for discre... more This note proposes a systematic approach for the static output feedback control design for discrete time linear systems. It is shown that if the open loop system satisfies some particular structural conditions, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the stronger
This chapter presents the different aspects of the design methodology that has been used to cope ... more This chapter presents the different aspects of the design methodology that has been used to cope with the RCAM design problem. A quadratic approach involving robust pole placement in a disk and the solution of parameter-dependent Riccati equations is proposed. Robustness as well as performance is accounted for by robust disk pole location that ensures robust stability and provides a good transient behaviour together with a specific selection of the weighting matrices involved in the Riccati equations.
Application de la commande robuste sequencee au controle de la transition operationnelle d’un sys... more Application de la commande robuste sequencee au controle de la transition operationnelle d’un systeme non lineaire Yann LABIT1, Pedro TEPPA1;2, Jacques BERNUSSOU1, Germain GARCIA1 1 Laboratoire d’Analyse et d’Architecture des Systemes du CNRS 7 Avenue du Colonel Roche, 31077 Toulouse, France 2 Universite Simon Bolivar, Valle de Sartenejas, Baruta, Caracas-Venezuelafylabit, pteppa, bernusoug@laas.fr Resume— Nous proposons, dans cet article, une approche systematique pour assurer la transition en stabilite d’un systeme dynamique non lineaire entre deux points operationnels. Ceci est realise dans un cadre d’un sequen- cement de lois de commande robuste issues de la satisfaction de contraintes en stabilite et en prenant compte de certaines specifications de perfor- mances locales qui restent valables dans un voisinage d’attraction d’un en- semble de points d’equilibre. L’approche proposee est implantee par l’in- termediaire de deux techniques : la premiere repose sur les fonctions cano- niques lineaires par morceaux tandis que la deuxieme se centralise sur des outils geometriques tels que les ellipsoi�
In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems... more In this paper, the problem of quadratic stabilizability of uncertain singularly perturbed systems by dynamic output feedback is addressed. Using a time-scale decomposition. two smaller-order ε-independent quadratic stabilizability subproblems are solved and it is shown that when ε is sufficiently small the combination of the corresponding results yields a quadratic stabilizing controller for the full order uncertain system, the controller being singularly perturbed itself with the same parameter ε as that of the system.
Uploads
Papers by germain garcia