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Original Articles

Unconstrained and constrained stabilisation of bilinear discrete-time systems using polyhedral Lyapunov functions

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Pages 2483-2493 | Received 11 Feb 2010, Accepted 09 Oct 2010, Published online: 13 Dec 2010
 

Abstract

The constrained and unconstrained stabilisation problem of discrete-time bilinear systems is investigated. Using polyhedral Lyapunov functions, conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second-order polynomial nonlinearities are first established. Then, systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented. Attention is drawn to the case where no linear control law rendering the pre-specified desired domain of attraction positively invariant exists. For this case, an approach guaranteeing the existence of a possibly suboptimal solution is established.

Acknowledgement

This article was supported in part by the Greek State Scholarships Foundation.

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