Control algorithm for uncertain discrete-time linear systems using concept of Ω-invariant

Deals with the control of uncertain discrete time linear systems with constrained state and control. Bounds on the structured perturbations are obtained to maintain stability using a Lyapunov approach matrix equation solution. The obtained bounds are shown to be restricted for systems with bounded controls and states. An approach is suggested to find a state constraint set for which the polyhedral is given in terms of the interaction of many maximal state constraint sets obtained from the nominal matrix system, including the vertices of the disturbance polyhedral. An interesting set is also given by using the Ω-invariant concept, thereby avoiding the solution of the Lyapunov equations