Guaranteed Cost Control Of Continuous-Time Uncertain Singular Time-Delay Systems With Indefinite Quadratic Cost

In this paper, the guaranteed cost control of continuous-time uncertain singular time-delay systems with indefinite quadratic cost is discussed based on Lyapunov theory and linear matrix inequality approach, the weighting matrix in the quadratic cost function is indefinite, it is only symmetric, may contain negative eigenvalue.First, in chapter one, the singular systerms, time-delay systems, uncertain singular time-delay systems, guaranteed cost control and related theories are introduced. Then research background and profound significance of this article are also introduced briefly.In chapter two, the state feedback guaranteed cost control of continuous-time uncertain singular time-delay systems with indefinite quadratic cost is investigated. First, based on Lyapunov theory, a condition is developed which guarantees that the closed-loop systems are regular, impulse-free, robust, sta-ble, and the state feedback guaranteed cost controller is existed. Next, by using some matrix inequalities to deal with the above sufficient condition, a linear matrix inequalities(LMI) sufficient condition is obtained, which guaran-tees that the closed-loop systems are regular, impulse-free and robust stable, the state feedback guaranteed cost controller is obtained directly by solving LMI. A numerical example is provided to illustrate the correctness and effec-tiveness of the proposed methods. At the same time, for the system without time-delay, the similar conclusions are obtained by corollaries.In chapter three, the static output feedback guaranteed cost control of continuous-time uncertain singular time-delay systems with indefinite quadratic cost is investigated. It is similar to the discussion in chapter two, based on Lya-punov theory, and by using singular value decomposition approach, a sufficient condition is developed firstly which guarantees that the closed-loop systems are regular, impulse-free and robust stable, the static output feedback guaranteed cost controller is existed. Next, a linear matrix inequalities(LMI) sufficient condition is obtained, which guarantees that the closed-loop systems are reg- ular, impulse-free and robust stable, the static output feedback guaranteed cost controller can be obtained directly by solving LMI. A numerical example is also provided to illustrate the effectiveness of the proposed methods. At the same time, for the system without time-delay, the similar conclusions are obtained by corollaries.The last chapter is the conclusion, in this chapter, a complete summary for studied questions, relevant theories and methods, and research ideas.