Input–output finite-time mean square stabilisation of stochastic systems with Markovian jump

Hongji Ma and Yingmin Jia

International Journal of Systems Science, 2014, vol. 45, issue 3, 325-336

Abstract: The notion of input–output finite-time mean square (IO-FTMS) stability is introduced for Itô-type stochastic systems with Markovian jump parameters. Concerning a class of random input signals W, sufficient conditions are presented for the IO-FTMS stability and stabilisation of stochastic nonlinear Markov jump systems in terms of coupled Hamilton–Jacobi inequalities. When specialising to the linear case, these criteria are turned into coupled linear matrix inequalities. Moreover, the quadratic IO-FTMS stabilisation is addressed when polytopic uncertainty appears in the transition rate. Finally, a numerical example with simulations is exploited to illustrate the proposed techniques.

Date: 2014
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DOI: 10.1080/00207721.2012.720299

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