Global Quadratic Stabilization in Probability for Switched Linear Stochastic Systems

Abstract

Global quadratic stabilization in probability is considered for both switched linear certain stochastic systems and switched linear uncertain stochastic systems where there are norm bounded uncertainties. Under the assumption that every single subsystem is NOT globally quadratically stable in probability (GQS-P), we propose both static and dynamic output based switching laws such that the switched system on hand is GQS-P. In the case of static output based switching, the condition is expressed by a set of matrix inequalities, while the design of dynamic output based switching is proposed with a convex combination of subsystems and a robust Luenberger observer for each subsystem. Numerical examples are presented to show validity of the design conditions and switching algorithms.

Keywords

• Switched linear certain stochastic systems (SLCSS)
• switched linear uncertain stochastic systems (SLUSS)
• norm bounded uncertainties
• convex combination
• globally quadratically stable in probability (GQS-P)
• output based switching