Mode-Dependent Fuzzy Control for Positive Fuzzy Markov Jump Systems with Guaranteed L_1-gain Performance

摘要

Positive fuzzy Markov jump systems (FMJSs) can describe dynamic systems with positive, nonlinear and stochastic features. The peculiar positivity makes a difference in the stability analysis and controller synthesis in contrast to general fuzzy systems and Markov jump systems. For the positive FMJSs, the definitions of exponential mean stability and L_1-gain performance are firstly introduced, and some stability and performance conditions are established in the form of linear programming, respectively. In special cases, these conditions can reduce to be the corresponding results of positive fuzzy systems and positive Markov jump linear systems. Then a mode-dependent fuzzy controller is designed such that the closed-loop fuzzy system is positive, exponentially mean stable and has prescribed L_1-gain performance. Finally, the control design validity is confirmed by a numerical example.