Robust quadratic stabilizability and \(H_{\infty}\) control of uncertain linear discrete-time stochastic systems with state delay (Q1793569)

Summary: This paper mainly discusses the robust quadratic stability and stabilization of linear discrete-time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is, respectively, obtained for the stability and stabilizability of the considered system. Moreover, we design the robust \(H_{\infty}\) state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust \(H_{\infty}\) controllable. A sufficient condition for the existence of the desired robust \(H_{\infty}\) controller is obtained. Finally, an example with simulations is given to verify the effectiveness of our theoretical results.