Generalized H_∞ performance and mixed H₂/H _∞ optimization for time delay systems

In this paper, a multi-objective optimization problem is investigated for a class of nonlinear continuous-time systems with time-varying delays. The controlled plant is supposed to have nonlinear dynamics and time delays which exist simultaneously in the state, the input and the measured output. To present the compatible mixed H₂/H_∞ control problem, the generalized H_∞, performance index is firstly introduced for the nonlinear delay systems instead of the standard H_∞ performance one. As such, the novel mixed H₂/H_∞ optimization problem can be formulated and the solvability conditions can be provided via convex computation approaches. After some algebraic transformations and decompositions, the involved nonlinear constraints can be eliminated and LMI-based convex algorithms can be given for the both state feedback and the output feedback design. These results can cover many previous works on the pure guaranteed cost control and the standard H_∞, control, and can be generalized to other multiple objective optimization problems with quadratic performance indexes.