Guaranteed Cost Control For Uncertain Generalized Delta Operator Systems

In the design of control system,it is a basic requirement to maintain the stability of the system,but in practical applications,the system generally has uncertainties.Uncertainties can have a lot of adverse effects on the system,not only to destroy some of the important performance of the system,and may make the system unstable.The goal of guaranteed cost control is to construct an ideal controller for the system with uncertainties,in order to ensure that the closed-loop system is stable or admissible for all admissible uncertainties,and its performance index exist the upper bound.The Delta operator model can provide a unified description for the two classes of continuous and discrete systems,so that many conclusions of the continuous system can be directly extended to the discrete system.On the other hand,the singular systems include singular continuous systems and singular discrete systems,which are widely used in practical production,and the results obtained in the singular continuous system are far more than the singular discrete system.Therefore,in the analysis and exploration of the singular system,the advanced Delta operator theory is applied to it,which will surely play a crucial role in promoting its research and development.At present,the relevant results of the singular Delta operator system can be seen mainly in the aspects of controllability,passivity and admissibility.The relevant research results of uncertain singular Delta operator system can be seen mainly concentrated in the robust H-infinity control,robust admissibility and robust non-fragility and so on.However,the related results of the guaranteed cost control problem for singular Delta operator system with uncertainties are rarely reported.In this paper,we study the robust guaranteed cost performance and control problems of uncertain singular Delta operator system.Firstly,the robust guaranteed cost performance is analyzed,and two sufficient conditions are derived based on matrix inequality and linear matrix inequality.Secondly,based on the above conditions,the existence conditions and design methods of the guaranteed state controller and guaranteed output feedback cost controllers are given respectively.Finally,the correctness and feasibility of the theoretical analysis results are verified by numerical examples and simulation curves.