Stabilization And Mixed H? And Passive Control Of Time-delay Rectangular Singular Systems

Descriptor systems,also called singular systems,can describe physical systems better than traditional systems,and have therefore received extensive research and attention from scholars.Rectangular descriptor systems,as a broader class of singular systems,have more complex behaviors because the number of state variables is inconsistent with the number of state equations.In practical engineering applications,the phenomenon of time-delay is common,and time-delay is often the main factor leading to the deterioration and instability of the system.Therefore,the study of time-delay dynamic systems has great value.In recent years,rectangular descriptor systems with time delay have begun to attract attention.Based on the existing research results,this thesis uses the Lyapunov functional method and new inequality technology to study the dynamic compensation of rectangular descriptor systems with time delay.A new delay-dependent stabilization and mixed H? and passive controller design scheme is proposed.Subsequently,this thesis uses an iterative algorithm to solve the controller gain matrix,and finally obtains conservative and less complex results.The main research results of this thesis are as follows:1.This work studies the stabilization of rectangular descriptor systems with time delay.Firstly,a time delay dynamic compensator is introduced to compensate the system,and then a suitable Lyapunov-Krasovskii functional is constructed,and advanced integral inequality is selected to deal with the functional derivative.Furthermore,the stabilization conditions of the rectangular descriptor system with time delay,expressed by strict linear matrix inequality(LMI),are obtained.Based on this,the iterative LMI-based algorithm is used to calculate the parameter matrix of the dynamic compensator and feedback gain.Finally,Numerical examples verify the effectiveness and superiority of this method.2.Aiming at the problem of mixed H? and passive control for rectangular descriptor systems with time delay,this work constructs a dynamic compensator with time delay and uses the admissibility criterion of a normal singular system in the real number field.Finally,sufficient conditions are obtained to allow the closed-loop system to be admissible under the conditions of mixed H? and passive performance index ?.This work constructed a suitable Lyapunov-Krasovskii functional,combined with the relaxed Wirtinger inequality,processed the integral term of the functional derivative,and replaced the non-linear term in the inequality.Using an iterative algorithm,the compensator is finally obtained gain matrix.Numerical examples verify the effectiveness of the method.