Robust State Estimation for T–S Fuzzy Markov Jump Systems

Abstract

The problem of robust state estimation for a class of uncertain nonlinear systems with Markov jump is investigated. The uncertain nonlinear system under consideration is represented by the Takagi–Sugeno (T–S) fuzzy model because it is difficult to describe. Firstly, different from the traditional T–S fuzzy modeling method, the deviation of the linear system approaching a nonlinear system is considered, which is represented as a model error in system modeling. Secondly, through a robust state estimation method based on the sensitivity penalty, we develop a robust state estimator for linear subsystems, and the fuzzy robust state estimator is obtained by fuzzy rules. Thirdly, the stability and boundedness of the fuzzy robust state estimator are proved under the assumption conditions to ensure the reliability of the obtained estimator. Finally, some numerical examples are given to verify the effectiveness of the fuzzy robust state estimator.