Singular Systems In A Few Questions

In the thesis , firstly the problem of static output feedback H∞control was explored for discrete time singular systems. Based on the generalized Riccati inequality and linear matrix inequality, necessary and sufficient conditions were obtained for the existence of static output feedback H∞controllers, which guarantees that the resulting closed-loop system is admissible with its transfer function matrix satisfying H∞norm constraint. Under some assumptions, a necessary condition was presented so that such controllers exist. Under certain condition, a sufficient condition was given such that the closed-loop system is admissible with its transfer function matrix satisfying H∞norm constraint. Secondly the H∞control problem based on dynamic output feedback for discrete singular systems is considered. With the generalized algebraic Riccati inequality (GARI) approach, a sufficient and necessary condition for the existence of dynamic output feedback H∞ controllers is presented, such that the resulting closed-loop system is admissible with its transfer function satisfying H∞norm constraint. Under certain assumptions, a necessary condition and a sufficient condition are derived for the existence of such H∞controllers. Thirdly we extend the definition of passive from nonlinear systems to discrete singular systems, and mainly concerns the passive control problem for discrete singular systems under bounded energy exogenous inputs. By means of linear matrix inequalities, a sufficient condition is given such that a prescribed discrete singular system is admissible and strictly passive. Moreover, under certain conditions, a static state feedback control law is designed such that the resulting closed-loop system is both admissible and strictly passive. The notion of strictly passive is proposed for discrete singular systems. This paper concerns the robust passive control problem for discrete singular systems with uncertain parameters under bounded energy exogenous inputs. By means of linear matrix inequalities, a sufficient condition is given for uncertain discrete singular system to be generalized quadratically stable and strictly passive, based on which, a sufficient condition is given for the existence of a state feedback controller, such that the resulting closed-loop system is both generalized quadratically stable and strictly passive for all the admissible uncertainties, All conclusions carry with them corresponding examples to prove the effectiveness, and the corresponding controllers are also presented.