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l2 state-feedback control with a prescribed rate of exponential convergence

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2 Author(s)
Fialho, I.J. ; Dept. of Aerosp. Eng., Minnesota Univ., Minneapolis, MN, USA ; Georgiou, T.T.

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, whereas 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

Published in:

Automatic Control, IEEE Transactions on  (Volume:42 ,  Issue: 10 )