Existence And Stability Of Solutions For Nonlinear Singular Systems

In many practical fields, it has been found that many problems are modelled by singular systems. Singular systems, also known as descriptor systems, semi-state space systems, differential-algebraic systems, and generalized state space systems, etc., arose when Rosenbrock analyzed electrical networks, in the course of describing dynamical processes with constraints. Their applications in optimal control problems and constrained control problems, electrical circuits, some population growth models and singular perturbations are wide. Over the past years, singular systems have caught people's great interest.This dissertation is composed of four chapters and mainly deals with the existence and stability of solutions for nonlinear singular systemsIn chapter one, the history of the study about singular systems is introduced accompanied with some prints of present work as well as the main work of this paper.In chapter two, by using monotone iterative technique combined with the method of upper and lower solutions, we discuss the initial value problems (IVP) of a class of nonlinear singular systems and a class of nonlinear discrete singular systems. The existence of solutions for nonlinear singular systems is obtained as limits of monotone sequence. Each member of those sequence is a solution of linear singular systems which can explicitly be computed.In chapter three, we use the same method as using in chapter two, and discuss the existence of solutions for the boundary value problem (BVP) of a class of nonlinear singular systems and a class of nonlinear singular systems with delay.In chapter four, we study the stability of solutions for the nonlinear singular systems with delay. We present new definitions of stability for singular systems with delay by using the thoughts of B.Baji'c and M.Mili'c, and establish theorem on stability. Then the sufficient conditions for uniformly stability of a class of special nonlinear singular systems with delay is given.