Limit cycles in delta-operator formulated 1-D and m-D discrete-timesystems with fixed-point arithmetic

Bauer P.H.; Premaratne K.

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Limit cycles in delta-operator formulated 1-D and m-D discrete-timesystems with fixed-point arithmetic

机译：三角运算符公式化的1-D和m-D离散时间系统的极限环定点运算

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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

机译：本文针对定点实现的情况，分析了由δ-算子制定的一维（1-D）和多维（m-D）离散时间系统的全局渐近稳定性问题。结果表明，如果使用传统的量化算术方案（例如截断或舍入），这种系统的自由响应会产生不适当的平衡点。根据采样周期，得出了全局渐近稳定性的明确必要条件。这些条件表明，在许多情况下，在使用短采样周期的δ算子公式化离散时间系统中，定点算术不允许全局渐近稳定性。一维和m-D情况均是如此

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《IEEE Transactions on Circuits and Systems. I, Regular Papers》 |1997年第6期|p.529-537|共9页
作者
Bauer P.H.; Premaratne K.;
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原文格式 PDF
正文语种 eng
中图分类 TN71;
关键词
asymptotic stability; digital arithmetic; discrete time systems; limit cycles; multidimensional systems; quantisation (signal); delta-operator formulation; discrete-time systems; equilibrium points; fixed-point arithmetic; free response; global asymptotic stability;

机译：渐近稳定性;数字算术;离散时间系统;极限环;多维系统;量化（信号）;delta-operator公式;离散时间系统;平衡点;定点算术;自由响应;全局渐近稳定性;

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1. Limit cycles in delta-operator formulated 1-D and m-D discrete-time systems with fixed-point arithmetic [J] . Bauer P.H., Premaratne K. IEEE Transactions on Circuits and Systems. 1 . 1997,第6期

机译：用定点算法在增量算子公式化的1-D和m-D离散时间系统中的极限环
2. A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic [J] . Vimal Singh Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2007,第3期

机译：利用饱和算法消除定点状态空间数字滤波器极限环的新频域准则
3. Limit cycles elimination in delta-operator systems [J] . Ralev K.R., Bauer P.H. IEEE Transactions on Circuits and Systems. 1 . 2000,第5期

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4. Limit cycles and asymptotic stability of delta-operator formulated discrete-time systems implemented in fixed-point arithmetic [C] . Premaratne, K., Bauer, . 1994

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机译：具有定点运算的Delta算子离散时间系统的极限环和渐近稳定性

Limit cycles in delta-operator formulated 1-D and m-D discrete-timesystems with fixed-point arithmetic

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