Structured robust stability and boundedness of nonlinear hybrid delay systems

Fei, Weiyin and Hu, Liangjian and Mao, Xuerong and Shen, Mingxuan (2018) Structured robust stability and boundedness of nonlinear hybrid delay systems. SIAM Journal on Control and Optimization, 56 (4). pp. 2662-2689. ISSN 0363-0129 (https://doi.org/10.1137/17M1146981)

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Abstract

Taking different structures in different modes into account, the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition. A new Lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes. Moreover, a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition.

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