Chattering free control of continuous-time switched linear systems

Abstract

Chattering is an undesirable phenomenon characterised by infinitely fast switching which may cause equipment damage in real systems. To avoid its occurrence, this study proposes a chattering-free switching strategy for continuous-time switched linear systems ensuring global asymptotical stability and a guaranteed cost level associated to the rms gain of a class of input to output signals. The switching function is designed considering a minimum dwell-time constraint in order to avoid chattering and a maximum one to ensure robustness with respect to sampling jitters and implementation imperfections as, for instance, delays in the switching process. The conditions are based on Riccati-Metzler inequalities which take into account an equivalent discrete-time switched linear system obtained from the continuous-time one guided by a sampled switching rule without any kind of approximation. As a new result, for a subclass of Metzler matrices, necessary and sufficient conditions for the existence of a solution for the Riccati-Metzler inequalities are provided. Theoretical aspects are illustrated by some academical examples.