Dynamic output feedback control with general form for incrementally quadratic nonlinear rectangular descriptor semi-Markov jump systems

This paper considers the dynamic output feedback control for a class of nonlinear rectangular descriptor semi-Markov jump systems (R-DSMJSs). There are no any constraints for the dimension of differential matrix, and the nonlinearities satisfy incremental quadratic constraints. A class of general rectangular dynamic output feedback controllers with free dimensions are designed, which can guarantee that the corresponding closed-loop systems are square descriptor semi-Markov jump systems (S-DSMJSs). First, sufficient condition is proposed to ensure that the closed-loop systems are regular, impulse-free, have unique solution, and are stochastically stable. Then a novel linear matrix inequality (LMI) sufficient condition is given based on the bounds of the time-varying transition rates and some matrix decoupling techniques, and controllers are obtained. Last, numerical examples are provided to demonstrate the effectiveness and advantages of the obtained methods and results.