## Abstract

In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

Original language | English (US) |
---|---|

Pages (from-to) | 529-537 |

Number of pages | 9 |

Journal | IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications |

Volume | 44 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 1997 |

Externally published | Yes |

## Keywords

- Delta operator
- Fixed point arithmetic
- Limit cycles
- Quantization error

## ASJC Scopus subject areas

- Electrical and Electronic Engineering