Dynamic Analysis Of Uncertain Switched Neural Networks With Time Delay

Neural networks are a large scale nonlinear dynamic system which are abstracted from the human brain neuron networks.A neural network is intrinsic a special form of parallel computer.Considering the switching happened in neural networks,some switched neural networks models are proposed.Since the highly interconnected architecture of switching neural networks provide a framework for designing massively parallel machines,which re-ceive considerable attention for their potential applications in many areas,such as image processing,pattern recognition,associative memories,solving certain optimization prob-lems,and so on.Switched neural networks constitute an important class of hybrid systems.Due to the existence of the switching rule,their dynamics may become very complicated.On the other hand,time delays and parametric uncertainty are unavoidable in practical engineering sys-tems,which may cause undesirable dynamical behaviors such as instability and oscillation.In addition,the analysis and synthesis problems become more complex.Therefore,it is significant to take time delay and parametric uncertainty into the models of switched neural networks.The main research contents of this paper are presented as follows.Exponential stability for a class of uncertain switched neural networks with time-varying delay is investigated.By exploring the mode-dependent properties of each subsys-tem,all the subsystems are categorized into stable and unstable ones.Based on Lyapunov-like function method and average dwell time technique under a prescribed limit to the max-imum activation time ratio,some delay-dependent sufficient conditions are derived to guar-antee the exponential stability of considered uncertain switched neural networks.Compared with general results,our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable,thus getting less conservative criteria.The passivity and finite gain L2 stability analysis problems for a class of uncertain switched neural networks with time-varying delay are addressed.We discuss the relation-ship between input energy,stored energy,and output energy of the uncertain switched neural networks with time-varying delay.Based on the Kalman-Yakubovich-Popov Lemma,the sufficient time delay-dependent criterion for passivity is established by Linear Matrix In-equalities(LMIs).Furthermore,an intensive study of the state strictly passive,input strictly passive,output strictly passive and L2 stability are made.Compared with the existing re-sults,our theoretical model is more general,and the conclusion is more practical.The robust state estimation problem for a class of uncertain switched neural networks with time-varying delay is studied.A more general class of switching signals,the persistent dwell-time switching is considered rather than the dwell-time or average dwell-time switch-ing often studied in the literature.By constructing a proper Lyapunov-like functional which is not only mode-dependent but also time-dependent and a new bounding technique,a delay-dependent sufficient condition is developed to guarantee the global exponential stability of the augmented error system and the corresponding designs of state observers are proposed.It is worth pointing out that the criterion is still valid when the lower range of time-varying delay of the switched neural networks is not zero.Moreover,a sufficient condition is pre-sented to guarantee the global exponential stability of the augmented error system when the time-varying delay of the system is not differentiable.The robust H? control problem for a class of switched neural networks with para-metric uncertainties and time-varying delay is discussed.A mode-dependent average dwell time(MDADT)method together with a Lyapunov-like function and reciprocally convex approach are adopted to the analysis and synthesis of H? control problems.And some delay-dependent sufficient criteria to guarantee that the corresponding uncertain switched neural networks with time-varying delay is globally exponentially stable un-der a weighted H? performance attenuation level are derived.Furthermore,a set of mode-dependent dynamic state feedback controllers and the MDADT for admissible switching signals are designed,which guarantees that the resulting closed-loop uncertain switched neural networks are robustly exponentially stabilizable with weighted H? per-formance.Finally,a numerical example is given to verify the validity of the obtained theory.