Robust State Feedback Controller Design Method Guaranteeing Deterministic H_∞ Performance and Stochastic Stability

Abstract

In this paper, we consider a design method of state feedback controllers for discrete-time linear systems with stochastic parameters that vary accordingly to independent and identically distributed (i.i.d.) process. If the parameters obey the normal distribution, then we cannot strictly guarantee the “conventional deterministic control performance” due to the unlimited parameter variations. Then, we propose incorporating the “stochastic stability”, which has been confirmed to be equivalent to quadratic stability in stochastic sense, into the conventional deterministic H_∞ performance. We derive a design condition on state feedback controllers that achieve deterministic H_∞ performance and stochastic stability simultaneously via extended linear matrix inequalities (LMIs) approach. The effectiveness of the proposed method is illustrated through a numerical example.