Robust stability condition and controller design for uncertain time-delayed discrete-time systems

The problem of robust stabilization is solved for discrete-time uncertain systems with multiple state delays the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The aim is to design a stable linear state feedback controller assuring asymptotic stability irrespective of the uncertainties and the time delays. A new robust parameter-dependent stability condition is proposed and corresponding controller design is presented in terms of linear matrix inequalities (LMI), which can be efficiently solved by the so called interior point algorithms. Compared with earlier results based on quadratic stability notion, the method is less conservative, which is illustrated by numerical examples.