ℋ∞ robust control of discrete‐time systems based on new linear matrix inequality formulations and evolutionary optimization.

This study presents novel formulations for ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust state‐feedback control synthesis for discrete‐time linear time‐invariant systems based on linear matrix inequalities. The proposed formulations require searching for two adjustment matrices. The synthesis formulations include other formulations from the literature as particular cases according to specific values of the adjustment matrices. We propose the application of evolutionary optimization to determine the optimal values of these two adjustment matrices. One approach to obtaining a single‐step formulation for static output‐feedback control synthesis is to transform a state‐feedback control synthesis formulation via the simple change of variables. The alteration of variables considered in this study requires an adjustment matrix. The adjustment matrix influences the performance of the resulting controller or the existence of a feasible solution to the problem. Here, we also propose the application of evolutionary optimization to determine the optimal value of this adjustment matrix and the two adjustment matrices of the proposed formulations to obtain the optimal ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust control system. Case studies verify that despite the increased complexity, the proposed formulations and the method required to tune them may be indispensable in achieving a robustly stable control system or an enhanced ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance for more intricate problems. [ABSTRACT FROM AUTHOR]