Robust H∞ Finite-Time Control for Discrete Markovian Jump Systems with Disturbances of Probabilistic Distributions

This paper is concerned with the robust H ∞ finite-time control for discrete delayed nonlinear systems with Markovian jumps and external disturbances. It is usually assumed that the disturbance affects the system states and outputs with the same influence degree of 100%, which is not evident enough to reflect the situation where the disturbance affects these two parts by different influence degrees. To tackle this problem, a probabilistic distribution denoted by binomial sequences is introduced to describe the external disturbance. Throughout the paper, the definitions of the finite-time boundedness (FTB) and the H ∞ FTB are firstly given respectively. To extend the results further, a model which combines a linear dynamic system and a static nonlinear operator is referred to describe the system under discussion. Then by virtue of state feedback control method, some new sufficient criteria are derived which guarantee the FTB and H ∞ FTB performances for the considered system. Finally, an example is provided to demonstrate the effectiveness of the developed control laws.