Finite time stability with guaranteed cost control for linear systems

This paper defines an optimal quadratic cost bound as a performance index for linear time varying systems subject to a finite time stability constraint. In particular, a sufficient condition for achieving such a guaranteed cost bound satisfying simultaneously the finite time stable constraint is given in terms of differential linear matrix inequalities. This condition is then exploited for the design of a state feedback control which make the closed loop system finite time stable with a guaranteed cost bound as the performance index. This leads to the design of an optimal controller under finite time stability constraint in the realm of convex optimization by the solution of a suitable feasibility problem. The applicability of the proposed approach is illustrated by means of an example showing the control of an inverted pendulum.