Linear quadratic control for sampled-data systems with stochastic delays

Abstract

We study optimal control for sampled-data systems with stochastic delays. Assuming that the delays can be modeled by a Markov chain and can be measured by controllers, we design a control law that minimizes an infinite-horizon continuous-time quadratic cost function. The resulting optimal control law can be efficiently computed offline by the iteration of a certain Riccati difference equation. We also obtain sufficient conditions in terms of linear matrix inequalities for stochastic stabilizability and detectability, which are used for the optimal controller design.