l1 state-feedback control with a prescribed rate of exponential convergence

In this paper we present sufficient conditions for the existence of state-feedback controllers that achieve a level of l¹ performance subject to the constraint that the unforced closed-loop is exponentially stable with a prescribed rate of convergence. A constructive algorithm is developed to compute an upper-bound for the achievable constrained performance. A variable structure linear controller that achieves this bound is presented. We show that, if certain orthogonality conditions are satisfied, this upper bound is actually equal to the achievable constrained performance. For an illustrative example that satisfies these conditions, we can construct controllers, that achieve an arbitrarily fast rate of convergence, without sacrificing input-output performance.