Estabilização via realimentação estática de saída de ciclos limites para sistemas afins com comutação a tempo discreto

Abstract

This paper deals with control design of a static output-dependent switching function for discrete-time switched affine systems to ensure global asymptotic stability of a suitable limit cycle. In a first step, a family of limit cycles that satisfy some performance criterion of interest is determined. This criterion is designed by the designer and is related to the steady-state response, as for instance, the maximum ripple. Afterwards, based on a time-varying convex Lyapunov function, a set of convex sub-problems, expressed in terms of linear matrix inequalities, is provided to determine an output-dependent switching function. This function must be associated to the limit cycle, inside the family of possible ones, that minimises an upper bound to the H2 performance index. An academic example is used for validation and comparison.