Limiting Behavior Of Linear Singularly Perturbed Systems: Analysis And Design

In this. dissertation, by means of the further investigation of the limitingbehavior of linear time invariant (LTI) singularly perturbed systems we discuss theproblem of the applicability of the singular system theory and synthesisapproaches in the-control design of singularly perturbed systems. This limitingmodel of a singularly perturbed system is of the form of the singular systems,while nowadays, the theory of singular systems is well developed and thus pavesthe way to develop a possible new synthesis approach to singularly perturbedsystems. However, because of the controlled plant models is different, singularsystem theory cannot be applied into singularly perturbed systems in general.Hence, via survey of the algebraic condition that the limiting solution is availableto approach that of the singularly perturbed systems, the limiting models areemployed to design controller for their original singularly perturbed systems. Thedesired performance is thus achieved by feedback controller that is designed basedon the limiting system model. The major works in this dissertation are as follows.Firstly, the limiting behavior of the solution of singularly perturbed controlsystems is discussed in distributional sense. Some improved conditions areproposed based on the existing results, under which, the solution of linear timeinvariant (LTI) singularly perturbed systems converges to that of the limitingsystem in distributional sense.Secondly, the singular system models are employed to analyze the H_∞propertyof singularly perturbed systems. The conventional design techniques of the outputdynamic feedback and state feedback H_∞controller for singular systems areimproved to suitable for singularly perturbed systems. It is shown that when suchan improved controller is applied to corresponding singularly perturbed systems,the stability and H_∞performance of the closed loop can be guaranteed.Thirdly, the singular system models are implemented to analyze the robuststability property of singularly perturbed systems. The conventional designtechniques of the state feedback robust stabilization controller for singularsystems are further improved to stabilize the original singularly perturbed system.Fourthly, the singular system models are applied to analyze the strictly positive realness property of singularly perturbed systems. The relationship between thepositive realness of singularly perturbed system and that of its limiting system isobtained.Finally, the problem of H_∞model reduction is investigated for singularlyperturbed control systems. An algorithm is proposed for the construction ofreduced model based on the slow-fast decomposition of original system.