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Original Articles

Computation of transfer function matrices of periodic systems

Pages 1712-1723 | Received 01 Jan 2003, Accepted 06 Oct 2003, Published online: 21 May 2010
 

Abstract

We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles-gain representation. A basic computation is the minimal realization of special single-input single-output periodic systems, for which both balancing-related as well as orthogonal periodic Kalman forms based algorithms can be employed. The main computational ingredient to compute poles is the extended periodic real Schur form of a periodic matrix. This form also underlies the solution of periodic Lyapunov equations when computing minimal realizations via balancing-related techniques. To compute zeros and gains, numerically stable fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations. Numerical examples computed with MATLAB-based implementations show the applicability of the proposed method to high-order periodic systems.

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