### Abstract

This paper studies the solution of the steady-state error covariance equation (which is represented by the algebraic Lyapunov equation) associated with a forward-pass fixed-interval smoother for discrete-time linear systems. A necessary and sufficient condition is given to assure the existence of a unique stabilizing solution. A simple algorithm for solving such an equation is also proposed by using four eigenvector matrices, which are generated by a symplectic matrix, corresponding to the algebraic Riccati equation of a backward-pass information filter. Thus the results have application to the important problem of the limiting covariance analysis of smoothing prior to practically dealing with a finite interval of data.

Original language | English |
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Pages (from-to) | 136-140 |

Number of pages | 5 |

Journal | Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME |

Volume | 108 |

Issue number | 2 |

Publication status | Published - Jun 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Instrumentation