Analysis And Synthesis Of Discrete-time Systems With Unknown Parameters

An important class of uncertain systems is of parameter-uncertain type, deeply studying for them has not only theoretic value, but also engineering significance. analysis and synthesis of stability and robust control of this system is worth for theory, and also has been more and more recognized by engineering. Based on the theory of Linear Matrix Inequality and Lyapunov stability, problems of stability and disturbance attenuation were investigated in detail in this thesis for linear uncertain discrete-time systems whose parameters belong to polytopic domains. This kind of system is simply called as polytopic uncertain systems. Majority of investigations concentrate on continuous-time systems rather than discrete-time systems, so the polytopic uncertain discrete-time systems are mainly investigated in this paper, in particular, time-varying systems.Quadratic stability has an important meaning on the research of robust stability for uncertain systems, which manages the whole group of systems by one alternative Lyapunov function. Even though every members of the group of systems are stable, the common Lyapunov function is hardly worked out to satisfy every members. In other words, the results based on quadratic stability have great conservativeness. To reduce the conservativeness, we select parameter-dependent Lyapunov functions to overcome the oneness of independent Lyapunov functions and take good use of the information of the upper bounds of the rate of variation or parameter increments, in particular, for time-varying systems. It's so called the approach of parameter-dependent Lyapunov function, which obviously has less conservative results.There are two steps to investigate polytopic uncertain discrete-time systems in this paper. (1) For constant parameter-dependent systems, respectively, using the approaches based on independent Lyapunov function and parameter-dependent Lyapunov function, robust stability and disturbance attenuation of this kind of systems are analyzed and synthesized; then state feedback controller and output feedback controller are designed. (2) For parameter-varying systems, the same investigation before-mentioned has been done; emphatically, information of the upper bound of parameter increment has been considered, when we compute increment of parameter-dependent Lyapunov function for parameter-varying situation. Conservativeness of the results can be reduced however the results are more complicated, in particular, for slowly-varying parameters. Constant parameters can be regarded as the extremeness of time-varying parameters when the upper bounds of parameter increments tend to zero; Independent Lyapunov function can be regarded as parameter-dependent Lyapunov function when the upper bounds of parameter increments tend to infinity. Therefore, for parameter-varying systems, the results based on the approach of parameter-dependent Lyapunov function have universality.The above results are all confirmed with examples. Through comparing the results of the examples, the approach of parameter-dependent Lyapunov function could reduce conservativeness of the results, and could educe the extremeness of parameters.