Robust Quadratic Stabilizability and H∞ Control of Uncertain Linear Discrete-Time Stochastic Systems with State Delay

Abstract EN

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∞ state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H∞ controllable.

A sufficient condition for the existence of the desired robust H∞ controller is obtained.

Finally, an example with simulations is given to verify the effectiveness of our theoretical results.