Robust Passivity And ISS Analysis And Control For Uncertain Singular Systems

This dissertation is devoted to the problems of robust strict passivity, ISS analysis and control for an uncertain singular system. Singular systems are dynamics systems governed by the combination of algebraic and differential equations. These systems arise naturally in dynamic models in a wide range of engineering applications such as:chemical engineering systems, electrical and mechanical systems, mechanical modeling, air craft modeling and economic systems, etc. For the past forty years, it has gained a great achievement in developing systematic, techniques for analyzing and designing the problem of singular systems. As uncertainty always exist in system modeling; it needs further investigation and improvement on the robust control of singular systems.In this dissertation, a robust strict passivity, ISS analysis and control for an uncertain singular system are studied while LMI techniques are utilized.In Chapter three, the robust strict passivity, ISS analysis and stabilization prob-lem for linear singular system with uncertainty is presented. This result is achieved by proposing LMI condition such that the resulting system is proved to be robust strict passivity and ISS. In addition, a state feedback controller is designed such that the resulting closed loop system is proved to be ISS if the proposed LMI condition is not fulfilled.Finally, an example is given to demonstrate the effectiveness of the proposed result.In Chapter four, the robust strict passivity, ISS analysis and control problem for singular system with nonlinear perturbation,where the nonlinearity is not nec-essarily small is investigated. By proposing a proper LMI condition, the robust strict passivity and ISS is proved. In this work, it can be seen that the maximum perturbation bound is any positive real number not restricted between zero and one. Furthermore, a state feedback controller is designed such that the resulting closed loop system is proved to be robust strict passivity and ISS if the proposed LMI condition is not satisfied.Numerical example is given for the effectiveness of the proposed result.In Chapter five, the robust strict passivity and absolute ISS analysis and feed-back problem for Lur’e singular systems with time invariant sector nonlinearities of exogenous disturbance is considered. A proper LMI condition is proposed such that the corresponding system is proved to be robust strict passivity and absolute ISS. Moreover, a state feedback controller is designed and the resulting closed-loop system is proved to be robust strict passivity and ISS with respect to the exogenous input if the either proposed LMI condition is not satisfied or the linear part of the system is not Hurwitz. Numerical examples are given for the effectiveness of the proposed results.This dissertation is the first research work in the current literature to use robust strict passivity, ISS analysis and control theory to study uncertain singular systems. It is our hope that this work will pave the way for further studies on the robust analysis and control of uncertain singular systems.