ℋ2guaranteed cost control for uncertain discrete-time linear systems
- 1 April 1993
- journal article
- research article
- Published by Taylor & Francis in International Journal of Control
- Vol. 57 (4) , 853-864
- https://doi.org/10.1080/00207179308934418
Abstract
The ℋ2 guaranteed cost control problem is analysed for uncertain, discrete-time linear systems. It consists on the determination of a constant state feedback stabilizing matrix gain and an ℋ2-norm upper bound which holds for all feasible models. Two different approaches are considered. The first is based on the optimality conditions provided by Bellmans's dynamic programming equation. The second is based on the geometric properties of the aforementioned problem. It is shown that it is possible to parametrize all stabilizing gains over a convex set. In this special parameter space, the ℋ2 cost is found to be a linear function of the free parameters. Finally, some relationships between these approaches are presented and numerical examples given.Keywords
This publication has 7 references indexed in Scilit:
- On a Convex Parameter Space Method for Linear Control Design of Uncertain SystemsSIAM Journal on Control and Optimization, 1991
- A linear programming oriented procedure for quadratic stabilization of uncertain systemsSystems & Control Letters, 1989
- Robust state feedback stabilization of discrete-time uncertain dynamical systemsIEEE Transactions on Automatic Control, 1988
- On the robustness of optimal regulators for nonlinear discrete-time systemsIEEE Transactions on Automatic Control, 1987
- A procedure for simultaneously stabilizing a collection of single input linear systems using non-linear state feedback controlAutomatica, 1987
- An easy way to find gradient matrix of composite matricial functionsIEEE Transactions on Automatic Control, 1981
- Adaptive guaranteed cost control of systems with uncertain parametersIEEE Transactions on Automatic Control, 1972