State feedback synthesis for discrete-time linear systems with stochastic parameters guaranteeing deterministic H₂ performance and stochastic stability

In this paper, we propose a design method of state feedback controllers for discrete-time linear systems whose state-space matrices contain stochastic parameters. For such systems, if the parameters fluctuate according to the normal distribution, it is impossible to strictly guarantee the “conventional deterministic control performance” due to the unlimited parameter variations. Then, in our problem setup, we consider incorporating the “stochastic stability” into the conventional deterministic H₂ performance. We derive a design condition on state feedback controllers which achieve deterministic H₂ performance and stochastic stability simultaneously in terms of linear matrix inequalities (LMIs) via extended LMI. The effectiveness of the proposed method is illustrated through a numerical example.