Stochastic Discrete-time Systems with Delay - Robust Vertex-dependent H∞ State-feedback Control

The theory of stochastic state-multiplicative state-feedback control of retarded discrete-time systems is extended to the robust polytopic case, where a vertex-dependent approach is applied. The latter problem is solved by first deriving a stability condition for uncertain systems based on the application of the Finsler lemma to the studied systems, where a special Lyapunov function is applied to each vertex of the uncertainty polytope. Compared to the stability condition which is obtained by the quadratic approach where a single Lyapunov function is applied to the whole uncertainty polytope, the vertex-dependent approach achieves a significatively less-conservative result than the former approach. Based on the vertex-dependent stability condition, a robust bounded real lemma is derived and solved, leading to the solution of the state-feedback control for uncertain systems.