Robust Control Of Affine Nonlinear Uncertain Systems

Robust control of nonlinear systems is a relatively novel direction and a central problem up to now. There has been a great deal of rich results in such field for the time being. Based on existent literature, we will make developed differential geometry theory and functional differential equation theory as our main mathematical tools to start with our work in this paper. This paper is mainly concerned with robust H~, control of nonlinear systems, robust stabilization of nonlinear systems with time梔elay, and as a special case, robust H~ control of linear time梔elay systems with more general uncertainties, which include the case with nonlinear uncertainties that can be transferred into linear case to deal with. These are given in detail as the following: As a new result of nonlinear control with Ha., idea, ~e have considered robust Hr,, control for nonlinear systems with neutral? type uncertainties under an engineering application background. Based on HJI inequality, state feedback and dynamic output feedback are given, respectively. By considering the difficulty of resolving of HJI inequality, our results are transformed into NLMIs for more efficient computation. In order to avoid resolving of HJI inequality completely, when robust H,~ control of an affine nonlinear uncertain system is considered, We make a transformation of HJI inequality with a construction of corresponding solution and a tectonic criterion, so that such difficulty is almost avoided. State feedback and dynamic output feedback are given too. The result of dynamic output feedback ?III ? LII 眫4~ case is easy to verify and far precede old one. lie successively discuss design on robust stabilization controller of uncertain nonlinear time梔elay systems based on differential geometry theory. An improved Razumikhin lemma and Lyapunov theory are applied and two controllers are given with and without nonlinear time梔elay uncertainty, respectively. A numerical example is also showed to test our results. Our technique is concerned with some achievements of nonlinear functional analysis. We are sure that robust controller of nonlinear time delay in this paper is considered for the first time. An LMI梑ased control method is presented to meet the requirement of controlling unstable fixed pointed of nonlinear uncertain time? delay chaotic sys~tems. Sufficient conditions for the existence of the time梔elay feedback controller has been obtained. Similarly, we discuss the tracking problem by applying the time梔elay feedback control. And a numerical example is provided to show the effectiveness of our results. Compared with nonlinear case and as special one, time梔elay linear systems with more general uncertainties are considered. Robust stabilization and robust H~control problems on multi梔elay uncertain systems with all disturbances are studied. LMI is introduced into robust H~ control problem in the corresponding systems. Our results are indicated as Riccati inequalities or LMIs. And the essential principle of this kind method is analyzed. By using an improved Razumikhin lemma, the limitations of bounds of delay functions? derivatives in past literature are also removed, the corresponding results on robust stabilization and robust H~~control problem are obtained, too.