离散线性状态饱和控制系统的稳定性

主要研究了一类含有饱和状态的离散线性系统的稳定性问题。系统的状态是该时刻标称系统状态的饱和函数,用系统的状态与该饱和函数做差,得到一个死区函数。借助该函数,通过引入一个适当的附加矩阵,利用李雅普诺夫理论和饱和函数的定义,给出了闭环系统在原点大范围渐近稳定的充分条件。应用矩阵理论,将非线性矩阵不等式化为线性阵不等式,并以矩阵的形式给出了控制器的设计方法,再利用Matlab工具箱求解矩阵不等式,最后,给出数值计算和仿真算例。

Stability of discrete linear control systems with saturating state

The stability problem for discrete linear control systems and state saturation is discussed.The state of the system is a state saturation function of the nominal system at the moment,which uses the system state and the saturation to make difference,in order to get a deadzone function.With the help of the function,introducing a new additional matrix as well as using Lyapunov theory and saturated function definition,this paper gives that the sufficient condition which guaranteed the closed-loop systems is asymptotic stability in the large at the origin.Through the application of matrix theory,this paper transforms nonlinear matrix inequality into linear matrix inequality,and provides controller’s design procedures in terms of matrix inequalities,and then uses Matlab toolbox to solve matrix inequality.At last,the numerical results and simulation examples are given.