基于均衡实现的离散广义系统模型降阶

Model Reduction Based on Balanced Realization for Discrete-Time Singular Systems

研究离散广义系统尤其是非因果子系统的模型降阶问题·首先对原系统进行系统变换,将降阶问题归结于只对非因果子系统进行化简,从而达到真正的广义系统的模型降阶,即保留系统原有的非因果性·然后分析了广义系统的可控性和可观性,且用Hankel奇异值的大小来衡量对应状态的可控程度和可观程度·结果表明,在均衡实现的系统中,较小的Hankel值所对应的状态的可控性和可观性都'较弱',从而为模型降阶提供了理论依据·最后对离散广义系统给出了一种新的降阶算法·数值仿真证明了该算法的有效性·

A model reduction for discrete-time singular systems especially the non-casual subsystems was investigated. A system transformation should be done first for the original system to enable the reduction problem to become merely as a simplification of the non-casual subsystems,thus getting a true model reduction of singular systems, i.e., retaining all the original non-casual attributes. Then,the controllability and observability are analyzed and they are weighed up in their corresponding states using the magnitude of Hankel singular values. The results showed that both the controllability and observability in the state corresponding to the smaller Hankel singular values are weakened. Based on it, a new reduction criteria is put forward with a new model reduction algorithm given. A numerical simulation illustrates the effectiveness of the proposed algorithm.