Abstract
This article studies a new criterion for the induced l∞ stability of fixed-point state-space digital filters without overflow oscillations and instability due to finite word length effects. The criterion not only guarantees exponential stability but also reduces the effect of external interference to an induced l∞ norm constraint. We present a numerical example, which demonstrates the effectiveness of the proposed criterion.
Highlights
When designing a linear time-invariant digital filter using a fixed-point arithmetic, one encounters quantization and overflow nonlinearities
The following question arises: is there an induced l∞ stability condition for digital filters with external interference and saturation arithmetic? as far as we are aware, for the induced l∞ stability for digital filters with external interference and saturation arithmetic, there are no results published in the literature so far
4 Conclusion This article studies a new criterion for the induced l∞ stability of fixed-point statespace digital filters with external interference and saturation overflow arithmetic
Summary
1 Introduction When designing a linear time-invariant digital filter using a fixed-point arithmetic, one encounters quantization and overflow nonlinearities. Several researchers have studies stability criteria for digital filters employing saturation overflow arithmetic [1,2,3,4,5,6,7,8]. It is important to study an alternative criterion that can overcome the shortcomings of existing stability criteria for digital filters.
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