EXACT COMPUTATION OF THE INFIMUM IN H-INFINITY-OPTIMIZATION VIA STATE FEEDBACK

This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the standard H infinity-optimal control with state feedback. The problem formulation is general and does not place any restrictions on the direct feedthrough term between the control input and the controlled output variables. The algorithm involves solutions of two algebraic Lyapunov equations of a subsystem obtained from the transformation of the original system into a special coordinate basis. The method is applicable to systems where the transfer function from the control input to the controlled output is right-invertible and has no invariant zeros on the j-omega axis. Two applications are also considered. The first one provides a necessary and sufficient condition for the solvability of H infinity-almost disturbance decoupling problem via state feedback with internal stability. The second application deals with the computation of the supremum of the complex stability radii which can be achieved by linear state feedback. Several examples are provided to illustrate the numerical algorithm, one of which is the determination of the achievable reduction in H infinity-norm of aircraft responses to turbulence in a disturbance rejection design using optimal state feedback, and another example is the achievable H infinity-performance in control of a flexible mechanical system.