Multiobjective h2/H∞ control design subject to multiplicative input dependent noises

This paper addresses the mixed H2/H∞ control problem for linear discrete-time systems with structured multiplicative input noises. The structured random noises are modelled by a diagonal matrix where individual multiplicative noise is allowed to be different. The Nash game methodology is adopted to deal with such a multiobjective control problem, and a necessary and sufficient condition is analytically given in terms of two cross-coupled modified algebraic Riccati equations (MAREs). Based on the stabilizing solutions to MAREs, bounded causal equilibrium strategies are thus conducted and the resulting control law optimizes some specific performance together with a guaranteed worst case performance. Some relevant issues that can be regarded as special cases of the problem under consideration are also discussed. Moreover, a numerical example is included to show the validity of the present results