## ABSTRACT

In this chapter we continue to study the H
_{2}/H
^{∞} control for discrete-time stochastic systems with multiplicative noise, which have many applications, for example, in networked control [187, 199, 201] and power control in CDMA systems [153]. Compared with discrete-time stochastic systems with additive noise [138], the H
_{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 [65], where a very useful SBRL was given in terms of LMIs, which has played an important role in H∞ filter design [78]. For the system dealt with in [65], the finite and infinite horizon mixed H
_{2}/H
^{∞} control problems were investigated in [208] and [207], respectively. Similar to linear continuous-time Itˆo systems, the existence of mixed H
_{2}/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.