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

摘要

The notion of input-output finite-time mean square (IO-FTMS) stability is introduced for Ito-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.