On Positive Realness for Stochastic Hybrid Singular Systems

On Positive Realness for Stochastic Hybrid Singular Systems

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This paper deals with the problem of passivity analysis and passivity-based synthesis for continuous-time stochastic hybrid singular systems (SHSSs).First, a set of Scimitar linear matrix inequalities for the stochastic admissibility and passivity, which is also known as the positive real lemma, is obtained for continuous-time SHSSs.The proposed condition successfully holds a necessary and sufficient condition for the positive realness of SHSSs, whereas the existing papers in the literature have been handled only sufficient conditions.Next, the passivity-based control synthesis problem is also considered based on the new positive real lemma.The passivity-based stabilization criterion for the closed-loop system with its mode-dependent state-feedback control is expressed in terms of matrix inequality.

Thus, by introducing an additional slack matrix to the non-convex conditions, the feasible conditions for the control gain Scraper Tool Set are obtained in terms of linear matrix inequalities.Finally, a numerical example is provided to show the effectiveness of the result.