Sliding Mode Control of Uncertain Systems with Distributed Delay: Parameter-Dependent Lyapunov Functional Approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed delay systems with polytopic-type uncertainties in this paper by applying the parameter-dependent Lyapunov functional method combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system. Then the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are also developed. The results are all given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.