## Abstract

A state-space algorithm for computing the solution of the 2-block superoptimal distance problem (SODP) is presented. Given a rational and antistable matrix function R(s) = [R_{11}(s)R_{12}(s)], find all stable approximations Q(s) that lexicographically minimize the singular values of the error function E(s) = [R_{11}(s)R_{12}(s)+Q(s)]. Conditions are given for which the superoptimal approximation is unique. In addition, an a priori upper bound on the MacMillan degree of the approximation is given. The algorithm may be stopped after minimizing a given number of singular values. This premature termination of the algorithm carries with it an expected saving in the computational effort and a predictable reduction in the MacMillan degree of the approximation. The algorithm only requires standard linear algebraic computations and is, therefore, easily implemented.

Original language | English |
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Pages (from-to) | 1115-1134 |

Number of pages | 20 |

Journal | SIAM Journal on Control and Optimization |

Volume | 31 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics