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Stochastic stabilization of hybrid differential equations

Deng, Feiqi and Luo, Qi and Mao, Xuerong (2012) Stochastic stabilization of hybrid differential equations. Automatica, 48 (9). pp. 2321-2328. ISSN 0005-1098

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Abstract

This paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system. New methods are developed and sufficient conditions on the stability for hybridstochasticdifferentialequations are provided. These results are then used to examine stochasticstabilization by stochastic feedback controls. Two types of structure controls, namely state feedback and output injection, are discussed. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. A couple of examples and computer simulations are worked out to illustrate our theory.