State Feedback Generalized H₂ Control For Singularly Perturbed Time-varying Delay Uncertain Control System

The main issue that the controlling system needs to address is the systematic analysis and design.To design a calibration controller which enables the closed-loop system to maintain its internal stability while bringing out the certain performance index of the system is a hotspot in the current controlling research field.The main performance index adopted includes H₂,H_?,L₁and L₂-L_?,the controlled issue on the performance index of L₂-L_?is defined as general H₂control.General H₂control is an important branch of the modern control theory which has evolved into a powerful tool in dealing with uncertain non-linear system.General H₂control allows an actual control system to remain asymptotic stability in the uncertainty situation with time-varying delay,meanwhile,the performance index of L₂-L_?can meet the requirement.As a consequence,general H₂control theory,whose performance index is based on the Euclidean norm of the system,is capable of achieving better dynamic and stable performance,hence,some practical problems existing in the control field will be effectively addressed,and its successful application in communication,internet control,industrial production as well as aviation aerospace industry and facilitating development of the society.Its advantage lies in not only its ability to conduct research on the stability of the non-linear system,but also the controller's design with a set of systematic methods when performing the systematic analysis and designing the controller.At present,plenty of scholars have utilized T-S model or Lyapunov stability theory to carry on the research of general H₂control in the fuzzy system,continuous system and discrete system,however,their research did not take time delay into consideration.Since the controller is in the same system with the controlled object,it is unreasonable to request the controller to achieve accurate results with the sole consideration of the uncertainty on the object when there are all kinds of uncertainties.Furthermore,quite amount of the researches only engaged in the uncertainties or singular perturbation condition without the study of time-varying delay,so the researches are neither comprehensive nor systematic unification.In some literatures,the sufficient judging condition just meet the requirement of some perturbation parameter instead of a steady singular perturbation range or there is potential for the singular perturbation range to expand when the closed-loop system becomes asymptomatically stable.In view of above,this thesis uses the existing theories as the theory base,based on Lyapunov stability theory,matrix data analysis chart and linear matrix inequality,this thesis will research on General H₂control with singular perturbation of both control input and interruption input with time-varying delay to the uncertain control system.The core contents are briefly expressed as follows:First,there will be the overview of the theoretical background and previous researches of General H₂control system from the time-varying delay and singular perturbation.And then,relevant lemmas are introduced,in the meantime,mathematical notations and abbreviations are explained.Second,as for the time varying and delay and singular perturbation controlling system with input control and interruption,a general H₂controller with memory will be designed and a new definition of general H₂performance index will be introduced.Next,a new quadratic Lyapunov functional relying on time delay and perturbation parameter will be selected.Assisting of the new lemma and cross-term definition method,the sufficient criteria of the general H₂stability will be deduced under the time-delay dependence and time-delay independence,the judging theorem of the specific design of the controller with memory will be exposed as well.The research on general H₂memoryless control of the system will be put out,meanwhile the general H₂control theory will be deepened under the situation of memory with feedback to deduct the sufficient criteria of general H₂stability in the corresponding closed-loop system.The new lemmas will be applied both cases of the time-delay dependence and time-delay independence to obtain the relatively less preservative stability judgment.The result will be disposed by linearization to eliminate its uncertainty,the stability judgment of general H₂control constructed into linear matrix inequality will be acquired,which will point out when the closed-loop system is asymptomatically stable ranging from zero and the singularly perturbed limit,by the way,the range of general H₂stability is expanded and performance index of L₂-L_?reduced.Eventually,the abovementioned theory will be promoted in the meantime the time-delay dependence and independence of linearization will be deduced,the new cross-term definition method will be applied to deepen the theory thereafter.The validity and feasibility of the method obtained in the dissertation will be verified with the selected numerical examples,all criterium can be dealt with and solved conveniently with Matlab toolbox.The corresponding comparison of the stable index with related articles will demonstrate the advantage of the methods adopted in this treatise considering its less conservative,and it's appropriate to standard and non-standard cases.