Abstract

Dissipative linear time-invariant (LTI) systems represent a large class of systems, which include bounded real, positive real and sector bounded systems as special cases, In this paper, a sufficient condition is developed for stability of the feedback interconnection of two dissipative LTI systems. The stability result generalizes and unifies previous stability results such as small gain, passivity and sector-boundedness theorems. State-space characterization of dissipative LTI systems is presented in terms of a dissipativity lemma, which extends the positive realness (Kalman-Yakubovich), bounded realness and sector-boundedness lemmas. These conditions are equivalently expressed as linear matrix inequalities.

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