Zunhai Gao
Model reduction, MIMO system, projection method, canonical form of block diagonal controllability, Krylov subspace
Large-scale systems and their model reduction have always been an active field. To solve the problem of order reduction in multiple input multiple output (MIMO) time-invariant linear systems, a new method for obtaining simplified models is proposed using the canonical form of block diagonal controllability and Krylov subspace. First, when the system is completely controllable, it can be transformed into a canonical form of block diagonal controllability by a nonsingular linear transformation. Then the transformed equivalent model is simplified by the Krylov subspace method and projection method. If the minimum polynomial of the system matrix is n, when the degree of reduction is greater than or equal to n, the reduced system can maintain all poles of the original system. When the reduction is less than n, the Krylov subspace method can be used for model reduction. In this way, the reduced model can be obtained theoretically with any order. The combination of the controllable canonical form and the Krylov subspace method is better than only the projection method or the Krylov subspace method, and numerical simulation shows the effectiveness of this method.
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