Persistent bounded disturbance rejection for uncertain time-delay systems

This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems with parametric uncertainty by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L₁-performance analysis are given in terms of linear matrix inequalities (LMIs). Based on the results, a simple approach to the design of a linear state-feedback controller is presented to stabilize robustly the uncertain time-delay systems and achieve a desired level of disturbance attenuation. All the obtained conditions are delaydependent. A numerical example is included to illustrate the proposed method.