Finite-time stochastic stabilisation of Markovian jump non-linear quadratic systems with partially known transition probabilities

This paper studies the problems of the finite-time stochastic boundedness (FTSB) and stabilisation for a class of discrete-time Markovian jump non-linear quadratic systems with incomplete information on transition probabilities. It is shown that the FTSB of the system can be ensured under some sufficient conditions derived. As a corollary, some sufficient conditions of the finite-time stochastic stability for the non-linear quadratic systems without exogenous disturbance are also established. Based on these results, stabilising mode-dependent state feedback controllers are designed for Markovian jump non-linear quadratic systems with/without exogenous disturbance, respectively. Consequently, the finite-time stochastic stabilisation problem is resolved. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory.