The Robust ¦É, For A Class Of Discrete Switched System <sub> 2 </ Sub>-¦É, <sub> ¡Þ </ Sub> Control

This thesis mainly deals with the robust l₂ — l_∞ control for discrete-time switched systems with uncertainty. The content can be cut into two parts:The first part: in this part, robust l₂ — l_∞, output feedback control problem is investigated for discrete-time switched systems. The parameter uncertainties are modelled as a fractional form, the norm-bound form is one of its special form. In this part, we mainly consider the following uncertain discrete-time switching system:By using switching Lyapunov function and linear matrix inequality (LMI) technology, a dynamic output feedback controller is developed and ensuring the closed-loop system is stable with l₂ — l_∞ norm bound. Where α_i(k) is the switching signal,which specifies which subsystem will be activated at certain discrete-time. Firstly, a sufficient condition is given to ensure the closed-loop system is stable with l₂ — l_∞ performance, and giving the method on how to design the controller, a numerical example is presented to demonstrate the application of the proposed method.The second part: the robust l₂ — l_∞ state feedback control problem is studied for the discrete-time switching system with delays. The parameteruncertainties are modelled as a fractional form. Consider the following system:JV TVt=l t=lJV JVJVt=lBy using switching Lyapunov function and LMI technology, a sufficient condition is developed to ensure the closed-loop system is stable with li — l^ norm bound, and giving the method on how to design the controller, numerical examples are presented to demonstrate the application of the proposed method.