A separation principle for linear switching systems and parametrization of all stabilizing controllers

13 years 11 months ago

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In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (ﬁnite) family of given conﬁgurations (Ai,Bi,Ci). We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current conﬁguration i. As a ﬁrst result, we provide necessary and sufﬁcient conditions for the existence of a family of linear compensators, each applied to one of the plant conﬁgurations, such that the closed loop plant is stable under arbitrary switching. These conditions are based on a separation principle, precisely, the switching stabilizing control can be achieved by separately designing an observer and an estimated state (dynamic) compensator. These conditions are associated with (non–quadratic) Lyapunov functions. In the quadratic framework, similar conditions can be given in terms of LMIs which provide a switching controller which has the same order of the plant....

Franco Blanchini, Stefano Miani, Fouad Mesquine

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