Robust Control Of Multi-time Delay Singular Systems With Linear Fractional Parametric Uncertainties

Time delay arises quite naturally in industrial and engineering systems, such as communication systems, biological systems, chemical systems and electrical networks. The existence of delay makes the system analysis and synthesis become more complicated and difficult. Meanwhile, delay is frequently a source of instability and performance degradation in many dynamic systems, and thus considerable attention has been paid to the research on the stability analysis and controller synthesis of time-delay systems. Singular system is a kind of dynamic system of more general and abroad applied background. It has been developed sufficiently from 1970s, and many results in the normal system have been extended to singular systems. In recent years, the investigation of singular systems has attracted a lot of attention, and some significant results have been obtained. And some new methods are presented. This paper mainly studies the problem of robust stability and stabilization for a class of time-delayed and multi-time delay singular systems and guaranteed cost control with linear fractional form parameter uncertainty. The main content may be summarized as follows:(1) The problem of robust stability and stabilization for uncertain continuous descriptor with state time-delayed is studied. Parametric uncertainty is assumed to be norm bounded. Necessary and sufficient conditions for generalized quadratic stabilization are obtained, when the LMI is satisfied, a desired robust state control law without time-delay can be constructed.(2) The problem of robust stability and stabilization for a class of time-delay singular systems with linear fractional parametric uncertainties is presented. Necessary and sufficient conditions for generalized quadratic stability are derived. The results generalize and improve previous works on delayed singular systems with norm-bounded parametric uncertainties.(3) It is addressed the robust guaranteed cost control problem based on state-feedback and static output feedback for time-delayed descriptor system with linear fractional form uncertainties via LMI approach.(4) The problem of robust stability and stabilization for a class of multi-time delay singular systems with linear fractional parametric uncertainties is presented. Necessary and sufficient conditions for generalized quadratic stability are obtained. The results generalize and improve previous works on time-delayed singular systems with linear fractional parametric uncertainties.Numerical examples are given at the end of each chapter to show the validity of each result.