Introduction and Literature Survey

This chapter is the introduction to Part II of the book. A short survey of the literature on delay-free and retarded systems with state- multiplicative noise is brought there. The robust control and estimation of delay-free systems with state-multiplicative noise is treated at the beginning of Part II. By applying Finsler’s lemma, a considerable improvement in the control design and estimation of these systems is achieved in the presence of large parameter uncertainties. Stochastic systems with time delay are then treated. Two approaches are offered to their control design. The first transforms the system to non-retarded system with norm-bounded uncertainty, that is, readily treated by previously known methods. The second approach is one that applies a predictor-based state-feedback control to time-delayed stochastic systems. At the end of Part II, a robust static output-feedback control is applied to retarded uncertain stochastic systems and also the theory of switching systems with dwell that has been developed in Part I of the book is applied to systems with state-multiplicative noise.