Exponential state estimation for Markovian jumping neural networks with discontinuous activation functions

This paper presents novel theoretical results on the exponential state estimation issue for Markovian jumping neural networks (MJNNs) with mixed time-varying delays and discontinuous activations. The jumping parameters are modeled as a continuous-time finite-state Markov chain. The nonlinear perturbation of the measurement equation are assumed to be locally Lipschitzian. By introducing triple-integral terms, the Lyapunov matrices in the Lyapunov functional are distinct for different system modes as many as possible. Based on the nonsmooth analysis theory and stochastic analysis techniques, a full-order state estimator is designed to make the corresponding error system exponentially stable in mean square. The desired mode-dependent and delay-dependent estimator can be achieved by solving a set of linear matrix inequalities (LMIs). Finally, one simulation example is given to illustrate the validity of the theoretical results.