一类线性时滞系统鲁棒控制器的设计

Design of Robust Controller for a Class of Linear Time-delay Systems

针对一类同时存在状态和控制滞后的线性不确定,时滞系统的鲁棒镇定问题进行了研究,其中系统的不确定项参数时变未知但范数有界,且滞后项也是时变的。对此,基于Lyapunov泛函,利用线性矩阵不等式给出了系统可由状态反馈鲁棒镇定的充分条件,并且利用线性矩阵不等式的解构造了使得系统鲁棒稳定的无记忆状态反馈控制律。所得结果是依赖时滞大小的,且与时滞的导数有关,从而相对减弱了控制器设计的保守性。最后通过一个例子说明了方法的有效性。

The problem of robust stabilization for linear uncertain systems with states and control delays was studied. The uncertain parameters are unknown and timevarying but normbounded, the delays are also timevarying. Based on the Lyapunov functional, sufficient condition for the robust stabilization via state feedback was presented in terms of linear matrix inequalities and a memoryless state feedback control law was constructed by using the solutions of the linear matrix inequalities. The result depends on the size of delays and includes information on the derivative of the delays, therefore the conservativeness of the controller design is reduced. Finally, an example is given to illustrate the proposed approach's effectiveness. 