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A new class of universal Lyapunov functions for the control of uncertain linear systems

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2 Author(s)
Blanchini, F. ; Dipartimento di Matematica e Inf., Udine Univ., Italy ; Miani, S.

We analyze the problem of synthesizing a state feedback control for the class of uncertain continuous-time linear systems affected by time-varying memoryless parametric uncertainties. We consider as candidate Lyapunov functions the elements of the class Σp z which is formed by special homogeneous positive definite functions. We show that this class is universal, in the sense that a Lyapunov function exists if and only if there exists a Lyapunov function in Σpz. We prove this result in a constructive way, showing that such Lyapunov function can always be obtained by “smoothing” a polyhedral function for which construction algorithms are available. We show how we can associate to the considered functions controllers in a global explicit form

Published in:

Decision and Control, 1996., Proceedings of the 35th IEEE Conference on  (Volume:1 )

Date of Conference:

11-13 Dec 1996

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