Superstable Linear Control Systems. II. Design

The notion of superstability introduced in [1] is applied to the design of stabilizing and optimal controllers. It is shown that a static output feedback controller which ensures superstability of the closed-loop system can be found (provided it exists) by means of linear programming (LP) techniques; finding a superstable matrix in the given affine family is a generalization of this problem. The ideology of superstability is also shown to be fruitful in optimal and robust control. This is exemplified by the problems of rejection of bounded disturbances, optimization of the integral performance index which involves absolute values (rather than squares) of the control and state, and by stabilization of an interval matrix family and simultaneous stabilization.