Chattering free control of continuous‐time switched linear systems. Issue 5 (1st March 2014) - Deaecto, Grace Silva; Souza, Matheus; Geromel, José C.
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.