### Abstract

This study represents a first attempt to derive a closed-form (Hankel-norm) optimal solution for multivariable system reduction problems. The major contribution lies in the development of a minimal-degree-approximation theorem and an efficient computation algorithm. The main theorem describes a closed-form formulation for the optimal approximants, with the optimality verified by a complete error analysis. Many useful singular value and vector properties associated with block Hankel matrices are also explored. The main algorithm consists of three steps: (i) compute the right matrix-fraction-description of an adjoint system matrix, (ii) solve a (algebraic) Riccati-type equation, and (iii) find the partial fraction expansion of a rational matrix.

Original language | English (US) |
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Pages (from-to) | 187-194 |

Number of pages | 8 |

Journal | Unknown Journal |

Volume | 1 |

State | Published - Jan 1 1980 |

Event | Unknown conference - Albuquerque, NM Duration: Dec 10 1980 → Dec 12 1980 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

*Unknown Journal*,

*1*, 187-194.