Guaranteed Cost Control For A Class Of Uncertain Discrete Time-delay Singularly Perturbed Control System

In the control system,the time delay and uncertainty are ubiquitous,such as network communication,petroleum processing,metallurgy and mechanical transmission,etc.For a discrete system,there are many factors to weaken the system performance and cause system instability,but the most important one is the time delay and uncertainty.In the related control theory research,the system performance index should meet certain preset requirements ensuring the robust stability,that is namely guaranteed cost control,one of the most important approaches to solve this problem in control field.In consequence,the research on it has both important theoretical significance and extensive applied value,and now it is the research hotspot and difficulty in the field of system control.How to design an efficient and reasonable guaranteed cost controller for uncertain discrete-time singularly perturbed control system with time delay while the performance index of the system will not exceed a certain upper limit at the same time of meeting the premise of comprehensive index is a challenging research topic attracted the attention of many scholars.At present,there are rich research results on guaranteed cost control for continuous systems,but still few for the uncertain discrete time-delay singularly perturbed control system.Based on the existing theoretical results,utilizing Lyapunov stability theory to research the guaranteed cost control problem of uncertain discrete-time singularly perturbed control systems with time delay by means of linear matrix analysis method and cross-term definition,and to deduce a smaller upper bound of performance index in this academic thesis,the specific contents are briefly summarized as follows:(1)Firstly,the theoretical background and research status of uncertain discrete time-delay singularly perturbed control system are introduced.In the meantime the guaranteed cost control problem is summarized in detail,and then the research purpose and main content of this dissertation are explained.(2)Secondly,to introduce the related lemmas,a memory state guaranteed performance controller is designed in terms of discrete singularly perturbed control system with uncertain discrete time delay and control input,a new definition to the performance index is constructed out as well as a new selected Lyapunov functional is given.Meanwhile,combing with the lemmas and Lyapunov stability theory,cross-term defined method,matrix analysis method and linear matrix inequality method and so on,the sufficient criterias of the guaranteed cost controller both delay dependence and delay independence are obtained.It is pointed out that the system is asymptotically stable in the whole range from zero to the upper bound of singular perturbation,the reduced upper bound of performance index and the extended guaranteed cost control range are showed.(3)Furthermore,the memoryless guaranteed cost control of the system is studied on the basis of memory to further deepen the above theory,and the corresponding sufficient condition inference is obtained.Subsenquently,a new cross-term definition is quoted to derive a less conservative controller design theorem.All the conclusions are eliminated the uncertainty,linearized in the form of linear matrix inequality,that can be easily solved by Matlab toolbox.After then,the enumerated examples are showed to illustrate the feasibility and effectiveness of the consequential conclusion,the superiority of the derived theorem control method is reflected by comparing the relevant literatures.(4)Finally,it summarizes the whole content,and states the theoretical content to be further improved in this dissertation,in addition,to remind of the shortcomings briefly and put forward the problems to be further studied in the next theoretical aspects.