Mixed H₂/H_∞ Optimal Control Problems For Singular Systems

In this thesis, we mainly discuss mixed H2/H∞optimal control problems for singular systems.Firstly, the problem of derivative and proportional state feedback mixed H2/H∞optimal control is explored for Singular systems. For a class of uncertain singular systems, the derivative and proportional state feedback controller is derived, thereby making the closed-loop system robustly stable, and in the meanwhile, makes sure that the H∞norm is norm-bounded and the upper bound of H2 norm is minimized. Then, a sufficient condition for the controller is given which is based on LMI method. Finally, a numerical example is presented in order to illustrate the effectiveness of the proposed method.Secondly, the problem of mixed H2/H∞optimal control based on LMI is investigated for discrete singular systems. The H2 control and H∞control performance is discussed respectively, in case of the system is admissible. Then, a state feedback of mixed H2/H∞controller is proposed which makes the closed loop system admissible, and it also makes sure the H∞norm is norm-bounded and the upper bound of H2 is minimized. Finally, a numerical example is given to illustrate the validity of the result.Lastly, the problem of mixed H2/H∞optimal control is explored for uncertain discrete singular systems. The H2 control problem and H∞control problem of robust stability is respectively discussed. Subsequently, a state feedback controller is designed, which makes the closed-loop system have the same performance. The sufficient condition which ensures that the system is robust stable and possesses mixed H2/H∞control performance is derived. Eventually, a numerical example is designed to demonstrate the effectiveness of the method.