The Research On Stabilization And Tracking Control For A Class Of Nonlinear Systems With Time-delays

Stabilization and the analysis and design of the tracking controller are two of the most important issues currently under consideration by researchers in linear and nonlinear control theory. The former addresses the convergence of system states to the origin or a bounded region containing the origin. The latter has two categories, output tracking and state tracking. The stabilization problem is a basic one, which stems from stability issues. When we discuss the stability of a system, taking into account the design of feedback controller problem, then the resulting stability problem is the Stabilization problem. Stabilization problem has being extensively studied for both linear and nonlinear systems. Whereas tracking control theory for linear systems is well established in the filed; for nonlinear systems, the controller design is a nontrivial problem, and is theory is still being developed. For nonlinear systems with time delays, stabilization and tracking problem is not perfect enough, has become a hot issue of control theories thus far.In this paper, we discuss stabilization and tracking control for a class of nonlinear systems with time delays and Lipschitz nonlinearities.Frist, we proposed a nonlinear tacking controller based on the state feedback. Using Lyapunov-Krasovskii stabilization theory and matrix theory, we obtain a new criterion on global asymptotic stability with delay-dependent based on linear matrix inequalities, which guarantees global asymptotic output and state tracking with zero tracking error in the steady state. Then we give a simulation example to show the feasibility of the theorem. Finally, we studied the delay-dependent stability theory and the tracking control problem of the above systems. In addition, this paper also equivalent to the extension of literature research model, by joining delay term, we respectively study its delay-dependent and delay-independent stability conditions. Therefore, this study model and the determinant conditions are more general and practical.