Multi-objective H2/H∞-optimal control via finite dimensional Q-parameterization and its applications

The problem of multi-objective H2/H_∞ optimal controller design is reviewed. A necessary condition is given to consummate the algorithm for the existence of a solution of the generalized non-symmetric and rectangular Riccatti equation. In view of the observer-based structure form of controller involving Youla parameter, the problem can be transformed into the tractable and practical LMI formulation of the multi-objective control problem through linearizing change of variables. In order to reduce the conservatism of the system, independent Lyapunov functions are used for each synthesis objective. Illustrative application to benchmark problem is given to demonstrate the useful and practicality of the approach.