This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
Performance robustness problems via the state feedback controller are investigated for a class of uncertain nonlinear systems with time-delay in both state and control, in which the neural networks are used to model the nonlinearities. By using an appropriate uncertainty description and the linear difference inclusion technique, sufficient conditions for existence of such controller are derived based on the linear matrix inequalities (LMIs). Using solutions of LMIs, a state feedback control law is proposed to stabilize the perturbed system and guarantee an upper bound of system performance, which is applicable to arbitrary time-delays.
