Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

In this paper, problems of finite-time boundedness are investigated for a class of discrete-time switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities. The time-varying transition probabilities are described by a piecewise-constant matrix subject to a high-level average dwell time (ADT) switching. Sensor and actuator saturations are characterized by a vector-valued decomposition method and the stochastic nonlinearities are approximated by a statistical method. In general, not all trajectories originating from the admissible initial states could be stabilized in the mean square sense or sufficient conditions are too restrictive to yield feasible solutions. Therefore, the purpose of studying the problems addressed here is to design an output feedback controller via the ADT approach such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation capability. Simulation results demonstrate the potential and effectiveness of the theoretical results.