H_∞ Control Of Discrete-Time Linear Systems With Time-Varying Delays

Time-delay and uncertainty which always exist in many actual systems:aerospace, chemical metallurgy,power networks and so on,make systems unstable and deteriorate systems' performance,due to insensitive measurement,signal transmission and parts ageing.The time-delay is an ubiquitous phenomenon in nature.It brings more complexity and trouble in analysis and synthesis,also result in instability of systems.Thus,it is significant to analyze the stability of systems with time-delay.In this paper,we discus H_∞Control problems of Discrete-Time Linear Systems by constructing a Lyapunov functional.In chapter 1,the research background of time-delay systems and H_∞control problems of such systems are introduced.Furthermore,the research problems, organizations and notations of this dissertation are also given.In chapter 2,we mainly deal with the H_∞control problems for discrete-time linear systems with time-varying delays in state and input.In this paper,the H_∞control law is assumed to be a memoryless state feedback,the size of timevarying delays is upper-bounded.The solution of the H_∞control problem for discrete-time linear systems with time-varying delays in state can be obtained by solving an H_∞control problem for auxiliary discrete-time linear systems without time-delay.In chapter 3,we mainly study H_∞control problem for discrete-time linear systems with time-varying delays in state and input in the same way in chapter 2.For the above two problems,we will obtain an effective feasible LMI solution of H_∞control problem.