非线性扰动的关联时滞广义大系统的二次稳定与H_∞控制

Quadratic Stability and Control for Large-scale Interconnected Time-delay Descriptor Systems with Nonlinear Perturbations

针对非线性扰动的关联时滞广义大系统,研究了其二次稳定性及H∞状态反馈控制器的设计问题。假设其中的不确定性是范数有界的,通过构造改进的Lyapunov泛函,给出了其二次稳定性及H∞状态反馈控制器存在的条件。仅通过求解相应的线性矩阵不等式(linear matrix inequality,LMI)就可得到鲁棒H∞控制器,设计的控制器对所有容许的不确定性不仅使得相应的闭环系统渐进稳定,也能保证闭环系统满足一定的H∞性能指标,达到抑制干扰的效果。最后,用数值算例及仿真验证了所给方法的有效性。

This paper focuses on the research of quadratic stabilization and H∞ controller designed for the large -scale interconnected time - delay descriptor systems with nonlinear perturbations. Based on the modified Lyapunov functions, under the assumption that the uncertainty is norm - bounded, existing conditions of quadratic stabilization and state feedback controller are given. The controller can be obtained by solving the corresponding linear matrix inequality. This controller designed can make the closed -loop systems asymptotically stable, as well as satisfying H∞ properties to achieve disturbance attenuation. At last, a numerical example and simulation testing are presented to illustrate the validity of this approach.