This paper mainly employed the methods which combined theoretical analysis with numerical simulation, MATLAB LMI Toolbox being computation tool. By employing Lyapunov stability theory and linear matrix inequality being research tool, interval time-varying delay system, multiple time-varying delays system, multiple time-varying delays system with nonlinear perturbations and robust stabilization design of linear system with input time delay and state time delay are studied.There are eight chapters in this dissertation:In Chapter 1, the research background of time delay system is firstly introduced briefly. Secondly, the stability analysis methods of time delay are reviewed. Finally, the main work of this dissertation and the used notations are listed.In Chapter 2, the basic knowledge and conception are introduced which are used in robust control research of time delay system. For example, Lyapunov stability theory and basic theorem, the basic theory of time delay system and several lemmas which will be used in the following chapter, which are theory foundation of the behind chapter.In Chapter 3, the stability criteria of interval time-varying delay system are studied. Constructing Lyapunov-Krasovskii functional based on the characteristic of time-varying delay for two cases, we have obtained delay-dependent stability criteria, and extended to delay-dependent and delay variety rate independent stability criteria. For the derivative of the Lyapunov-Krasovskii functional, by replacing with system function and holding x (t ), we obtain two different stability criteria, then which are extended to structure uncertainty and polytopic uncertainty.In Chapter 4, we continue to study the stability criteria of interval time-varying delay system. In virtue of the characteristic of interval time-varying delay, by disparting intervals [ -Ï„_{1}, 0] and [ -Ï„_{2} , -Ï„_{1}] into equal parts, we construct a new Lyapunov-Krasovskii functional which is mainly distinguished between the chapter 4 and chapter 3. By replacing with system function and holding x (t ), we also obtain two different stability criteria. From numerical examples, we can see there is superiority or inferior position between the chapter 4 and chapter 3. In Chapter 5, the stability criteria of multiple time-varying delays system are studied. We deal with the cross-term of the derivative of Lyapunov-Krasovskii functional by using integral equality, which is different to the famous free weighting matrix method, and preferably obtain the stability criteria of multiple time-varying delays system. Furthermore, we find integral equlity method is equivalent to free weighting matrix method for single time delay by comparing the stability criteria which obtained by the two methods, respectively. By replacing with system function and holding x (t ), we also obtain two different stability criteia, then which is extended to structure uncertainty and polytopic uncertainty.In Chapter 6, we continue to study the stability criteria of multiple time-varying delays system. The main difference is the cross-term of the derivative of Lyapunov-Krasovskii functional needn't be enlarged, but be holded the line, by improving free weighting matrix, and improving Lyapunov-Krasovskii functional. Numerical examples indicate that the stability criteria conservatism of chapter 6 is less than the stability criteria conservatism of chapter 5.In Chapter 7, the stability criteria of multiple time-varying delays system with nonlinear perturbations are discussed. Combining the multiple time-varying delays stability criteria of the chapter 6, using integral equality of chapter 2 and Newton-Leibniz formula, we obtain delay-dependent stability criteria, and extend to delay-dependent and delay variety rate independent case, Numerical examples indicate that the stability criteria conservatism of chapter 7 is less than the previous ones.In Chapter 8, we study robust stabilization design of linear system with input time delay and state time delay. Combining the multiple time-varying delays stability criteria of chapter 5, by using the free weighting matrices of inequality, we present a kind of linearization method, and preferably resolve robust stabilization design of the system. |