Finite-Time Control For Several Classes Of Nonlinear Systems

In control theory,finite time stability is presented in order to deal with robustness,anti-interference and transient performance of nonlinear systems.In this paper,we study the finite-time control problems of continuous-time uncertain nonlinear systems,uncertain Markovian jump nonlinear systems and T-S fuzzy jump neural networks.The main work is as follows:1)We mainly study uncertain bounded parameters and the finite time control problem of Markov jump systems with norm bound,uncertainties and partly unknown transition probability.Sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are provided for the class of systems by using stochastic analysis and linear matrix inequality methods.2)The finite time control of a class of uncertain continuous nonlinear systems is addressed.By using linear matrix inequalities and Schur complement properties,we prove the finite-time stability,finite-time boundedness and finite-time H? boundedness.3)We tackle the finite time filtering analysis and design problem of discrete-time T-S fuzzy neural networks with Markov jump parameters and bounded excitation functions.Firstly,in the absence of external perturbations,sufficient conditions on the finite-time stability are given for nominal fuzzy jump neural networks.Then,a finite-time filtering is designed such that the augmented fuzzy neural network systems without certain parameters are finite-time bounded.Thirdly,we provide the design strategy of uncertain augmented fuzzy neural network systems.Furthermore,all criteria obtained can be expressed as linear matrix inequalities.