In this paper we consider the ℓ1 -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ1 performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ1-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ1 performance.
Bibliographical noteFunding Information:
Manuscript received July 19, 1995; revised June 15, 1996 and October 21, 1996. This work was supported in part by the NSF under Grant NSF/ECS-9016050 and the AFOSR under Grant AF/F49620-92-J-0241. I. J. Fialho is with the Department of Aerospace Engineering, University of Minnesota, Minneapolis, MN 55455 USA. T. T. Georgiou is with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455 USA. Publisher Item Identifier S 0018-9286(97)05957-6.
- Controlled-invariant sets
- Isaacs equation
- ℓ control