Analysis Of State Characteristics Of Several Classes Of Neural Networks Based On Differential Inclusions

Based on differential inclusions, nonsmooth analysis, stochastic analysis theory andLyapunov method, this dissertation studies global robust exponential stability of almostperiodic solution of interval neural networks with discontinuous neuron activation, stateestimation of stochastic neural networks and synchronization control of memristiveneural networks. The main result of the dissertation is listed as follows:1. The robust almost periodic dynamical behavior is investigated for interval neuralnetworks with mixed time-varying delays and discontinuous activation functions. Firstly,based on the definition of the solution in the sense of Filippov for differential equationswith discontinuous right-hand sides and the differential inclusions theory, the existenceand asymptotically almost periodicity of the solution of interval network system areproved. Secondly, by constructing appropriate generalized Lyapunov functional andemploying linear matrix inequality (LMI) techniques, a delay-dependent criterion isachieved to guarantee the existence, uniqueness and global robust exponential stability ofalmost periodic solution in terms of LMIs. Moreover, as special cases, the obtainedresults can be used to check the global robust exponential stability of a unique periodicsolution/equilibrium for discontinuous interval neural networks with mixed time-varyingdelays and periodic/constant external inputs.2. The exponential state estimation issue for Markovian jumping neural networks withmixed time-varying delays and discontinuous activation functions is investigated. Thejumping parameters are modeled as a continuous-time finite-state Markov chain. Thenonlinear perturbation of the measurement equation is assumed to be locally Lipschitzian.By introducing triple-integral terms, the Lyapunov matrices in the Lyapunov functionalare distinct for different system modes as many as possible. Based on the nonsmoothanalysis theory and stochastic analysis techniques, the full-order state estimator isdesigned to make the corresponding error system exponentially stable in mean square.The desired mode-dependent and delay-dependent estimator can be achieved by solving aset of LMIs. 3. Study the synchronization control of a class of memristor-based recurrent neuralnetworks with time-varying delays and under stochastic perturbations. Withoutconsidering the definition of Filippov solution, based on the state-dependent switchingfeature of memristor, the error system is divided into four cases. Discontinuous statefeedback controller and adaptive controller are designed such that the considered modelcan realize globally asymptotical synchronization. Moreover, the design of state feedbackcontroller dependent on the switching jumping of memristor, and the design of adaptivecontroller is easily achieved without solving any inequality or LMI.