Simultaneous Stabilization And Control For Singular Systems With Time-delay

Singular system can described practical engineering and life background which was closely connection with human. Such as catalysis and cracked in petrochemical industry, population model, neural network, robotics, economic administration field. Due to the time delay phenomenon accompanys complex industrial manufacture process, the results that controlled object self sink system into instability condition.That's to say, researching singular system stabilization and control plays a very important role in control field. In fact, the designed controller not only makes sure the closed-loop system stable, but also satisfy expected performance requirement. Many systems simultaneous stabilization is also a major issue in systems and control theory, which has far-reaching significance on society development.This paper discuss simultaneous stabilization and control problem for finited singular systems with time delay from following several aspects:(1) The H-infinity control problem for a collection of singular systems with time delay is analysed. There are two methods of controller design. One is state feedback and the other one is observer-based dynamic output feedback.(2) Robust simultaneous H-infinity control problem for uncertain singular systems with time delay dependent is studied. The new bounded real lemma is given in terms of linear matrix inequalities(LMI) by introducing suitble Lyapunov-Krasovskii functional and Jesen inequality. Moreover, the simultaneous H-infinity controller sufficient condition with delay dependent is derived. Then approach of controller design is obtained.(3) The idea of Robust simultaneous H-infinity control problem for nonlinear singular systems with time delay is inquiried. State of systems is nonlinear and time-varying. Firstly, the free singular systems stabilization criterion is derived from Lyapunov-Krasovskii functional and LMI. sceondly, the sufficient condition of closed-loop nonlinear singular systems with time delay is gained via state feedback control to guarantee regular, impulse-free, simultaneous asymptotic stable. Finally, the H-infinity controller design approach is provided.(4) The simultaneous guaranteed cost control problem for a group of nonlinear singular systems with uncertain and time-delay is considered.The nonlinear item lay in finite Hurwctiz angular domain and uncertain parameters are norm bounded. Under the circumstance of state is time varying and bounded, according to need from paper, the definition of simultaneous guaranteed cost controller and the cost function is gave. A sufficient condition for the existence of simultaneous guaranteed cost controller is derived, which based on Lyapunov-Krasovskii functional and linear matrix inequality(LMI) approach. Furthermore, optimal guaranteed cost controller which minimizes upper bound of cost index function is exactly design by formulating the convex optimization problem.