Stability Analysis For Some Classes Of Dynamics Under Uncertainty With Applications

This paper is devoted to the study of the stability for some classes of dynamicsunder uncertainty.The first chapter is devoted to introducing some important background.In the second chapter, a new class of interval projection dynamics are introducedand studied, the equilibrium point of this dynamics is equivalent to the KT point ofa class of interval quadratic program. By using fixed point theorem and constructingsuitable Lyapunov functions, we obtain sufficient conditions to ensure the existence andglobal exponential stability for the unique equilibrium point of interval dynamics. In thelast section, we give an example to illustrate the validity of our results.In the third chapter, we introduce and study a new class of global set-valued pro-jected dynamical systems. By using the fixed point theorem due to Nadler and the pro-jection operator technique, we prove that the equilibrium points set of this class of globalprojected dynamical systems is nonempty and closed.In the fourth chapter, a class of interval general BAM neural networks with delaysare introduced and studied, which include many well-known neural networks as specialcases. By using fixed point technic, we prove an existence and uniqueness of the equilib-rium point for the interval general BAM neural networks with delays. By using a properLyapunov functions, we get a sufficient condition to ensure the global robust exponentialstability for the interval general BAM neural networks with delays, and we just requirethat activation function is globally Lipschitz continuous, which is less conservative andless restrictive than the monotonic assumption in previous results. In the last section, wealso give an example to demonstrate the validity of our stability result for interval neuralnetworks with delays. In the fifth and the sixth chapter, a class of interval BAM neural networks withmixed delays under uncertainty and a class of stochastic interval BAM neural networkswith mixed delays are introduced and studied, which include many well-known neuralnetworks as special cases. The mixed delays mean the simultaneous presence of boththe discrete delay, and the distributive delay. Furthermore, the parameter of matrix istaken values in a interval and controlled by a unknown, but bounded function. By usinga suitable Lyapunov-Krasovskii function with the linear matrix inequality (LMI) tech-nique and the stochastic analysis technique, we obtain a sufficient condition to ensurethe global robust exponential stability for the interval BAM neural networks with mixeddelays under uncertainty, and a sufficient condition to ensure the global robust exponen-tial mean square stability for the stochastic interval BAM neural networks with mixeddelays, respectively, which are more generalized and less conservative, restrictive thanprevious results. In the last section of the fifth and the sixth chapter, the validity of ourstability results are demonstrated by a numerical example, respectively.