基于LMI的连续时间线性时滞系统有限频模型降阶

LMI based approach for finite-frequency model order reduction of continuous-time linear time-delayed systems

针对连续时间线性时滞系统,研究了在系统工作频率范围为已知有限区间情形下的有限频模型降阶问题.通过引入有限频域内误差传递函数的最大奇异值函数作为指标函数,对模型逼近性能进行了刻画,进而结合一些基础性的矩阵不等式技术和线性时滞系统性能进行分析,得到了保持降阶模型稳定性的有限频模型逼近性能优化设计条件,这些条件以线性矩阵不等式(linear matrix inequalities,LMIs)的形式表示,易于检验和数值求解.最后,算例验证了结果的有效性.

Model order reduction of continuous-time linear time-delayed systems over limited frequency intervals is discussed in this paper. The approximation performance is char- acterized by introducing an index associated with the finite-frequency maximum singular value of the error transfer function. With the aid of some fundamental matrix inequality techniques, sufficient criterion for stability of the reduced-order model and optimizing finite-frequency approximation error is derived. The model order reduction problems can be tackled by solving the corresponding linear matrix inequalities （LMIs） based optimization problems. A numerical example is given to show effectiveness of the proposed technique.