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The problem of robust and guaranteed stabilization is addressed for switched affine systems using sampled state feedback controllers. Based on the existence of a control Lyapunov function for a relaxed system, we propose three sampled-data controls. Global attracting sets, computed by solving a sequence of optimization problems, guarantee practical and global asymptotic stabilization for the whole system trajectories. In addition, robust margins with respect to parameters uncertainties and non uniform sampling are provided using input-to-state stability. Finally, a buck-boost converter is considered to illustrate the effectiveness of the proposed approaches.Index Terms-Input-to-state stability, robust control, stabilization of hybrid systems, switched systems.

International audienceThis paper is dedicated to the modelling of LTI continuous time systems in digital control loops. We consider the digital control problem on non-uniform sampling periods. Moreover, we assume that time varying delays that may have a variation range larger than a sampling period affect the closed-loop. Our goal is to present a unique model that is able to include these problems simultaneously and that can be handled by classical control synthesis tools. We present a new event based discrete-time model (an exponential uncertain system with delay) and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system with an additive norm bounded uncertainty. The methodology is extended to the case of switched system

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In this article, a method for computing an optimal state feedback control law for continuous-time switched affine systems exhibiting cyclic behaviour in steady state is presented. The hybrid solutions are deduced from the Fillipov solutions. It is shown that the optimal trajectory synthesis implies to determine singular arcs. Algebraic conditions are given to obtain these particular arcs of the trajectory. A numerical procedure is then proposed to generate optimal trajectories on a given state space area avoiding the classical two-point boundary value problem occurring in optimal control synthesis. The interpolation of the solutions set, through a neural network, yields a state feedback control law. Several examples in the power converters field show the feasibility and the efficiency of the method.

Abstract-In this article, stability of continuous-time switched linear systems in the singular perturbation form is investigated. We show that the stability of slow and fast switched subsystems is not a sufficient condition for stability of the corresponding two-time scale switched system, under an arbitrary switching law. Thus, LMI conditions to design a statefeedback control law stabilizing continuous-time singularly perturbed switched linear systems are proposed.