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Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

✍ Scribed by Jamal Daafouz; Jacques Bernussou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
91 KB
Volume
43
Category
Article
ISSN
0167-6911

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✦ Synopsis

In this paper, we consider discrete time systems with polytopic time varying uncertainty. We look for a class of parameter dependent Lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter. We show that extending the new discrete time stability condition proposed by de Oliveira et al. (Systems Control Lett. 36 (1999) 135.) to the case of time varying uncertainty leads to a necessary and su cient condition for the computation of such a Lyapunov function. This allows to check asymptotic stability of the system under study. The obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem.

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