## Abstract

The paper brings a brief report on three new algebraic tests to determine whether a two variable polynomial has all its zeros inside the unit bi-circle (is 'stable'). A three-term recursion algorithm associates the tested two-variable polynomial with a sequence of matrices (the 2-D 'table') that possess a symmetry which allows to compute only half of the entries for each matrix. The recursions incorporate a deconvolution/division mechanism that removes recursively redundant common polynomial factors and prevents an exponential grow of the raw dimension of the matrices. A minimal set of conditions necessary and sufficient for stability for a polynomial with variables of degrees (n_{1}, n_{2}) requires one or two 1-D tests of degree n_{1} and the testing of whether a last 1-D polynomial has zeros in the real interval [-1,1] or on |z| = 1. The degree of this last polynomial is only 2n_{1}n_{2}.

Original language | English |
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Pages (from-to) | 5-8 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | Suppl |

State | Published - 1996 |

Event | Proceedings of the 1996 IEEE International Symposium on Circuits and Systems, ISCAS. Part 1 (of 4) - Atlanta, GA, USA Duration: 12 May 1996 → 15 May 1996 |