L1 fuzzy observer design for nonlinear positive Markovian jump system

This paper presents a positive L1 state-bounding observer which can estimate the state all the time for nonlinear positive Markovian jump systems. The considered system is represented by Takagi-Sugeno(T-S) fuzzy system. First of all, by constructing a linear co-positive Lyapunov function, the sufficient condition is obtained for stochastic stability and L1 performance analysis respectively. Furthermore, a positive L1 state-bounding observer for positive T-S fuzzy Markovian jump systems is designed. The conditions can be solved by linear programming. Finally, the results obtained are applied to the epidemiological model and illustrated to be better than the existing results by a numerical example.