Standard solution to mixed H 2 / H ∞ control with regular Riccati equation

In this study, the authors are concerned with the long-standing mixed H 2 / H ∞ problem for discrete linear systems. The main contribution is to derive the standard solution of the mixed H 2 / H ∞ problem by a regular Riccati equation. Firstly, in H ∞ -optimisation procedure, the optimal strategy ( u , w ) is explicitly given where the H ∞ -norm is maximised by w and H 2 -norm is minimised by u at the same time. It is noted that there exists an arbitrary item in the optimal strategy for the positive semi-definite weighting matrices. Secondly, the H 2 -optimisation problem is explicitly solved with respect to the arbitrary item. Finally, the standard solution of the mixed H 2 / H ∞ problem is explicitly given in terms of regular Riccati equations by combining the optimal strategy ( u , w ) in H ∞ optimisation procedure and the optimal solution of H 2 optimisation procedure. Examples are presented to show the effectiveness of the proposed approach.