Research On The Control Of Piecewise Discrete-Time Linear Systems

In this thesis, the systems stability, state feedback stabilization, output feedback stabilization of piecewise discrete-time linear systems are investigated deeply based on piecewise quadratic Lyapunov functions technique. The main contributions are as follows:Firstly, the judge conditions to the stability of uncertain piecewise discrete-time linear systems are presented. It is shown that the stability conditions can be cast as solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially available software such as Matlab. Furthermore, the work presented in this note can be considered as an extension of the work for the certain piecewise discrete-time linear systems.Secondly, the approach to the state feedback control for uncertain piece-wise discrete-time linear systems is presented. Based on the designed piecewise quadratic Lyapunov functions, the state feedback controller design is cast as the feasibility problem of a set of BMIs.Thirdly, the design of output feedback controller for uncertain piecewise discrete-time linear systems is presented. By constructing augmented polyhedral cell bounding matrix and augmented piecewise quadratic energy function, and using S-procedure lemma, the positivity of the function and the negativity about the time can be judged. Then it can be used as the piecewise quadratic Lyapunov functions of the systems. Based on the designed augmented piecewise quadratic Lyapunov functions, the dynamic output feedback controller design is cast as the feasibility problem of a set of BMIs.Finally, several examples are included to demonstrate the flexibility and power of the given approaches.