Robust finite-time bounded observer design for a class of uncertain non-linear Markovian jump systems

This paper concerns the state estimation problem for a class of uncertain non-linear Markovian jump systems, where the Markovian jump only occurs in some 'short' finite-time intervals. For this class of Markovian jump systems, the boundedness of estimation error deserves our investigation. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring uncertain non-linear Markovian jump system's finite-time stochastic stablility and boundedness are derived, then the result is extended to γ -disturbance attenuation case. Based on the analysis results, a robust observer ensuring the estimation error bounded with γ -disturbance attenuation in a prescribed boundary is constructed. A design algorithm is proposed when some parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.