Qualitative Studies Of Control Systems With Delay

Neural network is a nonlinear dynamic system composed of lots of processing cells(nerve cells).Recently,considerable attention has been devoted to the study of neural networks because they have been extensively applied in many areas,such as signal processing,optimization problem,pattern recognition,associative memories and so on.However,the information latching is a frequent occurrence that the considered neural network has finite modes by extracting finite state representation,and every mode corresponds to a deterministic system.The switching between these modes is dominated by a Markov chain,which is called Markovian jump neural networks.They can represent various physical processes that experience unexpected external disturbances,and abrupt changes in their structures,parameters and subsystem interconnections.Therefore,MJNNs have been a hot issue of various subjects.Now,state estimation and passivity analysis has become one of important issues to study MJNNs.In this thesis,based on Lyapunov-Krasovskii functional(LKF)theory,matrix decomposition method,Shur complement lemma,inequality techniques etc,performance analysis problem of several kinds of delayed control system is investigated.Some sufficient conditions are established which guarantee the stability and passivity of considered system.Finally,illustrative examples are provided to show the correctness and effectiveness of the methods and results.The following is the main research works in this thesis:1.The problem of state estimation for neural networks with leakage,discrete and distributed delays is studied.A method to remove the limitation of the derivative of discrete delay less than one is proposed without using activation function.Meanwhile,A new technique is given to show the stability of neutral system.Together with some new LKFs,convex polyhedron method and new activation function conditions,several sufficient conditions are derived which guarantee the stability of the error system.2.The problem of stability is studied for uncertain MJNNs with leakage delay,two additive time-varying delay components,and nonlinear perturbations.The Markovian jumping parameters in the connection weight matrices and two additive time-varying delay components are assumed to be different in the system model,and the Markovian jumping parameters in each of the two additive time-varying delay components are also different.Accordingly,a weak infinitesimal operator acting on LKF with two different Markovian jumping parameters is firstly proposed.The relationship between the timevarying delays and their upper bounds is efficiently utilized to study the suggested system in two cases: with known or unknown parameters.By constructing a newly augmented LKF and using the extended Wirtinger inequality and a reciprocally convex method,several sufficient criteria are derived to guarantee the stability of the proposed model.3.The problem of state estimation for two Markovian jumping NNs with leakage,discrete and distributed delays is studied.The Markovian jumping parameters in connection weight matrices and discrete time-varying delay are assumed to be different.Matrix decomposition method is firstly applied,which sufficiently utilizes the information of Lyapunov matrices.Combining with an appropriate LKF,the reciprocally convex approach and Wirtinger-based integral inequality,some sufficient conditions are established.They guarantee that the estimation error converges to zero exponentially in the means quare sense.4.The problem of passivity analysis for neural networks with two different Markovian jumping parameters,leakage delay,discrete delay and distributed delay is studied.The Markovian jumping parameters in connection weight matrices and discrete timevarying delay are assumed to be different in the system model.By constructing a new appropriate LKF and using some integral inequalities,which produce sharper bounds than what the Jensen's inequality produces,some sufficient conditions are established which guarantee the passivity of the proposed model.5.The problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling is studied.The Markovian jumping parameters,appearing in the connection weight matrices and in two additive time-varying delay components,are considered to be different.The controller is assumed to have either additive or multiplicative norm-bounded uncertainties.The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional.By using the matrix decomposition method and some newly inequalities,sufficient conditions are obtained to guarantee that the system is robustly stochastically passive.