ABSTRACT
This chapter investigates the robust stabilization and robust H8 control problems for a class of stochastic time-delay uncertain systems with Markovian switching and nonlinear disturbance. It aims to design a state feedback controller, which might also involve time-delay, such that for the considered nonlinear disturbances, Markovian switching and all admissible uncertainties, the closed-loop system is stochastically stable with a given disturbance attenuation level γ, independent of the time-delays. Sufficient criteria will be derived based on an linear matrix inequality (LMI) method, and a numerical example is given to illustrate the effectiveness of the author main results. H8 control problem for the same system is studied, then an LMI approach is developed to ensure the solvability of the problem and a direct design method is provided of the desired controllers. An illustrative numerical example is provided to show the effectiveness and usefulness of the proposed approach.
