ABSTRACT
This chapter discusses the H2/H∞ control for discrete-time stochastic systems with multiplicative noise, which have many applications, for example, in networked control and power control in CDMA systems. Compared with discrete-time stochastic systems with additive noise, the 2/H∞control of systems with multiplicative noise is more challenging. The study of the H∞ control for discrete-time systems with state- and disturbance-dependent noise seems to start from, where a very useful SBRL was given in terms of LMIs, which has played an important role in H8 filter design. For the system dealt with in, the finite and infinite horizon mixed H2/H∞ control problems were investigated. Similar to linear continuous-time Ito systems, the existence of mixed H2/H∞controllers for general discrete-time systems with multiplicative noise is equivalent to the solvability of four coupled difference matrix-valued equations. However, they differ in that the four coupled difference equations can be solved recursively.
