A Class Of Uncertain Nonlinear Systems, Robust Control,

It is known that Lur'e control system is a class very typical nonlinear control system, which has widely engineering background of the domain of aerocraft control and aviation control etc. Because of the characteristic of nonlinear, uncertainty and time-delay etc, the study to Lur'e control system takes on very complex peculiarity. Along with study of Lur'e uncertain time-delay control system with several stationary components is deepened, the robust control problem of Lur'e system with several stationary components is paid attention in the near future.By using norm inequality and Lyapunov functional method, Lur'e uncertain time-delay control system with a stationary component is considered above all in this paper. Sufficient conditions of the robust absolute stability of the system with structured parameter perturbations and norm bound parameter perturbations are given. When in the linear part of the plant, the uncertainties are known but norm-bounded, and the uncertainties in the nonlinear part satisfy the so-called matching condition, the nonlinear state feedback law of exponential stability for the system is obtained in the sense of global exponential stability. Furthermore, Lur'e uncertain time-delay control system with several stationary components is studied in this paper. The robust absolute stability bound and the delay bound of the system can be directly estimated. By analyzing the robust absolute stability, the design of nonlinear state feedback control law is obtained. In addition, the guaranteed cost control problem via memoryless state feedback controllers is considered in this paper for Lur'e control system with several stationary components, and sufficient conditions and the parameterized representation are given. In particular, the optimal guaranteed cost control law which minimizes the value of the guaranteed cost for the close-loop uncertain time-delay system can be determined by formulating and solving a certain convex optimization problem with several linear matrix inequalities(LMIs)constraints. Every important theorem is followed by corresponding numerical examples to illustrate feasibility and validity of the results.In this paper, it is outstanding regarded that the stabilities results are optimizedby using linear matrix inequality (LMI) . Because a lot of software as Matlab are widely application such that the operation of high dimension matrix becomes very easy, the theory results which are optimized by efficient interior-point optimization algorithms of linear matrix inequality (LMI) can be more accepted.