不确定时滞状态饱和系统的稳定性分析与综合

主要研究了不确定时滞状态饱和系统的稳定性问题。首先,假设不确定参数矩阵满足范数有界不确定结构,然后将系统的饱和函数项利用凸组合的方式表示。以凸组合形式的表示方法便于对饱和函数项进行适当的放缩处理,同时根据李雅普诺夫稳定性理论,给出了系统大范围渐近稳定的充分条件。通过变量变换和矩阵理论,将系统稳定的充分条件转化为Matlab软件可求解的线性矩阵不等式的形式,同时也给出了系统状态反馈控制器的设计方法。最后利用Matlab软件中的LMI工具箱求解线性矩阵不等式,得到使系统稳定的解矩阵,验证了结论的有效性和可行性。

Stability analysis and controller synthesis for uncertain time-delay systems with state saturation nonlinearities

The paper mainly study the stability problem of uncertain time-delay systems with state saturation nonlinearities.First of all,assume that the norm of the uncertain parameters matrix of state saturation system is bounded.Secondly,the saturation function item of the system is represented by convex combination.The representation method of convex combination form facilitates the proper scale of saturation function item.According to Lyapunov stability theory,the sufficient condition for the wide range asymptotic stability of systems is given.Further,based on variable transformation and matrix theory,the sufficient condition is transformed into the form of linear matrix inequality（LMI）which is solved by Matlab.At the same time,the state feedback controller which makes the system asymptotically stable is also designed.Finally the paper uses LMI toolbox of the Matlab to solve the linear matrix inequality,and gives the solution matrix for the stability of the system,thus the feasibility and effectiveness of the conclusion is verified.