Studies On Several Control Technologies Of Differential Inclusion Systems

Uncertainty usually exists in the nature. Differential inclusions usually can be used todescribe the system with uncertainty. This kinds of systems are more general than systemsdescribed by ordinary differential equations. For example, linear time-invariant systems,interval systems, polytopic systems, etc, can be taken as a special form of the differentialinclusion systems. For the differential inclusion system, how to construct the analysis andthe method of controller design has been an important topic in modern control theory.This paper mainly investigates several controller design methods of differential inclusionsystems.This paper consists of five chapters. The main contents of every chapter are as fol-lows:Chapter one is an introduction. It introduces the properties and the recent develop-ment of differential inclusions, gives a brief introduction about the models of differentialinclusion systems with special structures and some research approaches, then presentsbasic mathematical theories used in this paper. Finally, the major work of the paper issummarized.Chaper two considers the stabilization problem of differential inclusion systems viasliding mode control. First, the common systems are investigated, the models includea class of nonlinear systems and uncertain time-delay systems. For a class of nonlinearsystems, a new reaching law is proposed to reduce the chattering phenomenon. For theuncertain time-delay system with nonlinear input, an observer-based passive sliding modecontroller is proposed and sufficient conditions are obtained such that the looped system isasymptotically stable and passive. For polytopic differential inclusion systems and poly-topic stochastic differential inclusion systems, the sliding mode control approach is usedto design their controllers, respectively. Moreover, passivity is considered for the poly-topic stochastic differential inclusion systems. Finally, examples are given to illustratethe effectiveness of the proposed methods. Chapter three investigates the nonlinear state feedback controller design methods ofpolytopic linear differential inclusion systems with time delay and polytopic stochasticdifferential inclusion systems with time delay, respectively. Using the convex hull func-tion method, a nonlinear state feedback law is designed to stabilize the polytopic lineardifferential inclusion system with time delay. Then this technology is successfully ex-tended to the polytopic stochastic differential inclusion system with time delay, sufficientconditions are derived to guarantee the closed-loop system is exponentially stable in themean square.Chapter four proposes the finite time control problems for both polytopic linear dif-ferential inclusion systems and polytopic stochastic differential inclusion systems. Forthe polytopic linear differential differential inclusion systems, a generalized H2 controlleris designed not only to guarantee finite time boundedness of the closed-loop system, butalso to restrict the effect of disturbance on a prescribed level. For the polytopic stochas-tic differential inclusion systems, a state feedback law is designed to guarantee finite-timestochastically boundedness of the closed-loop system. Finally, observer-based non-fragilefinite time stabilization of Lur'e differential inclusion systems is investigated.Chapter five summarizes the main contents in this thesis and presents some valuableproblems.The main innovations of this dissertation can be summarized as follows:1) For a class of nonlinear systems, a new reaching law is proposed to reduce thechattering phenomenon. For the polytopic differential inclusion systems and the polytopicstochastic differential inclusion systems, sliding mode control approach is firstly used todesign the controllers, respectively. These results construct a theoretical framework of thepolytopic differential inclusion systems via sliding mode control.2) The method of convex hull of quadratics is successfully extended to stabilize thepolytopic linear differential inclusion system with time delay and the polytopic stochasticdifferential inclusion system with time delay. The results greatly enlarge the design scopeof nonlinear controller.3) A new feasible approach is proposed to design finite time controllers of both the polytopic linear differential inclusion systems and the polytopic stochastic differentialinclusion systems by the way of combining the descriptor system method and finite timecontrol. For the Lur'e differential inclusion systems, the design of observer-based non-fragile finite time controller is considered. By the design, the problem of finite timecontrol of this type of systems can be effectively resolved.