Analysis and Synthesis of Switched Linear Systems with Random Mode-Dependent Sojourn-Time

This paper concentrates on the issues of stability and stabilization for a class of switched linear systems with a new class of switching signals in discrete-time domain. The considered switching signals are of general random mode-dependent sojourn-time (RMST) property. Compared with the dwell-time switching or Markov chain often studied in the literature, it is capable of describing the mode-dependent sojourn-time consisting of a fixed part and a random part with the known expectation. By fully considering the characteristics of RMST, the criteria of stability and stabilization are derived for the underlying systems. Further, the results are extended to the asynchronously switched stabilizing control for RMST switched systems. A numerical example is provided to demonstrate the effectiveness and potential of the theoretical results.