### “A Recursive Algorithm for the Reduction of Block Diagrams”

**Authors:**Trond Andresen,

**Affiliation:**NTNU, Department of Engineering Cybernetics

**Reference:**1991, Vol 12, No 1, pp. 47-56.

**Keywords:**Block diagram reduction, recursive algorithm, transfer matrix, time delay

**Abstract:**A recursive algorithm to compute input-output relationships in a network of rational transfer functions (a block diagram) is derived. Initially all transfer functions are disconnected. For each step in the algorithm, a new transfer function in the network is connected to the system. One application of the algorithm is to find the transfer matrix of a linear multivariable system given on state space form. The algorithm is advantageous when one needs repeated computations of a transfer matrix in a multivariable system for successive changes in one or a few parameters in the system. The transfer matrix for a multivariable linear system with one time delay, and the exact frequency response in the case of several time delays, are derived.

PDF (982 Kb) DOI: 10.4173/mic.1991.1.4

**References:**

[1] HOROWITZ, I.M. (1963). Synthesis of Feedback Systems, Academic Press, N.Y. and London.

[2] OGATA, K. (1967). State Space Analysis of Control Systems, Prentice-Hall, N.-J.

**BibTeX:**

@article{MIC-1991-1-4,

title={{A Recursive Algorithm for the Reduction of Block Diagrams}},

author={Andresen, Trond},

journal={Modeling, Identification and Control},

volume={12},

number={1},

pages={47--56},

year={1991},

doi={10.4173/mic.1991.1.4},

publisher={Norwegian Society of Automatic Control}

};