Robust $ {\cal H}_{\infty}$ Control of a Class of Nonlinear Uncertain Time-Delay Systems

Abstract

The robust $ {\cal H}_{\infty}$ control problem of a class of uncertain nonlinear time-delay systems is considered in this paper. The parametric uncertainties are real time-varying and normbounded and the nonlinearities are state-dependent and cone-bounded. The delays are time-varying and bounded both in the state and at the input. We provide sufficient conditions for robust stability and robust state-feedback stabilization with disturbance attenuation. Then, we establish sufficient conditions for designing a linear dynamic observer-based controller which stabilizes the uncertain time-delay system and guarantees an $ {\cal H}_{\infty}$ -norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. Several examples are simulated to illustrate the developed theory.