Mixed H2/H∞ Control with Regular Riccati Equation

The mixed H
₂
/H
_∞
problem for discrete-time linear systems with positive semi-definite control weighting matrix is addressed in this paper. For regular system, the solution to the problem is given in terms of the solutions to regular Riccati equation. The regular Riccati equation is proposed to explicitly construct the optimal feedback control. In order to develop a systematic approach to this problem, each performance specification has been considered explicitly. In H∞ optimization procedure, the H
_∞
constraint with prescribed disturbance attenuation level is guaranteed by the obtained strategies. By matrix conversation, the arbitrarily items in the strategies are reformulated as strategies which are waiting to be solved in the procedure of minimizing H
₂
-norm. The novel contributions of this paper are as follows. First, by completing square method, necessary and sufficient conditions of the solution for this regular mixed H
₂
/H
_∞
control problem are given. Second, the arbitrarily items in the progress of H
_∞
optimization are converted into strategies which is waiting to be optimized in H
₂
optimization.