T–S Fuzzy Control of Positive Markov Jump Nonlinear Systems

The positive stochastic stabilization issue is investigated for Markov jump nonlinear systems. The nonlinear systems in the absence and presence of uncertainties are considered and modeled into Markov jump fuzzy systems with known and partially known membership functions, respectively. For the former, the parallel distributed compensator (PDC) controllers are designed to realize the positive stochastic stabilization. Besides, an additional criterion is derived to reduce the number of linear inequalities. For the latter, namely, some elements of membership functions are unavailable, and the PDC strategy is infeasible. Then, a switching controller, whose structure is parallel to that of fuzzy model, is constructed to achieve the corresponding positivity and stability. All the conditions are transformed to standard form of linear programming problem, which is solved with the help of linprog toolbox. Finally, the feasibility of the obtained results is illustrated by a pest's structured population model.