Static output feedback global asymptotic stability of limit cycles for discrete-time switched affine systems

Abstract

This paper deals with static output feedback stabilisation of suitable limit cycles for discrete-time switched affine systems. In a first step, a limit cycle is determined according to a performance criterion specified by the designer related to the steady-state response of interest as, for instance, the maximum allowed ripple. Afterwards, based on a time-varying convex Lyapunov function, a min-type switching rule is designed through sufficient conditions expressed in terms of linear matrix inequalities that ensure global asymptotic stability of the limit cycle and an H2 or H∞ minimum guaranteed cost. A practical application example concerning the voltage regulation of a DC-DC multicellular converter is used for validation and comparison.