Stability Analysis for Linear Systems with Time-Varying and Time-Invariant Stochastic Parameters

Abstract

This paper presents a method to guarantee stability of linear stochastic systems. The systems include both time-varying and time-invariant unknown stochastic parameters simultaneously. For analyzing the stability, such a system is represented by an expanded system that contains only the time-invariant stochastic parameter. This expansion excludes the time-varying parameter from the system, which simplifies the stability analysis. Existing methods on robust stability theory can be thus employed to ensure stability of the expanded system. Guaranteeing stability of the expanded system is a necessary and/or sufficient condition for that of the original system. Consequently, the stability of the original system is evaluated by using linear matrix inequalities.