滞后离散广义系统的鲁棒严格耗散控制

Robust strictly dissipative control for linear discrete delay singular systems

研究确定的及不确定的滞后离散广义系统的无记忆状态反馈严格耗散控制器设计问题.利用线性矩阵不等式(LMI)方法,首先给出滞后离散广义系统容许(即正则、稳定、因果)且严格耗散的条件,然后通过矩阵不等式(MIs)得到无记忆状态反馈严格耗散控制器的存在条件和设计方法;进而针对除E外其余系数矩阵均具有范数有界不确定性的滞后离散广义系统,利用矩阵不等式的解设计鲁棒严格耗散控制器,保证闭环系统广义二次稳定且严格耗散.

This paper deals with the design of memory-less state feedback strictly dissipative controllers for linear discrete delay singular systems with or without uncertainty.By using the approach of linear matrix inequality （LMI）,firstly a sufficient condition is presented for a prescribed linear discrete delay singular system to be admissible （i.e.regular,stable and causal） and strictly dissipative, then the existence condition with explicit expression of a memory-less state feedback strictly dissipative controller is derived in terms of matrix inequalities （MIs）. Furthermore, for an uncertain system where all coefficient matrices, except matrix E, contain norm-bounded uncertainties, a robust strictly dissipative controller is designed by using the solution of matrix equalities. This controller guarantees the resultant closed-loop system to be generalized quadratically stable and strictly dissipafive.