Finite-Time Observer Design for a Class of Markovian Jump Systems

Markovian jump systems are often used to model occurrence of failures and repairs in manufacturing systems. This note concerns the state estimation problem for a class of Markovian jump systems, where the Markovian jump only occurs in some short time intervals. For this class of Markovian jump systems, the boundness of estimation error deserves our investigation. By introducing the concepts of finite-time stochastic stability, an observer ensuring the estimation error bounded in a prescribed boundary is constructed and the result is extended to γ-disturbance attenuation case. A design algorithm is proposed when some parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.