Stability of digital filters subject to external interference and state-delay

2020 ◽  
Vol 42 (13) ◽  
pp. 2559-2568
Author(s):  
Priyanka Kokil ◽  
CG Parthipan
Keyword(s):  
Asymptotic Stability ◽  
Numerical Simulations ◽  
Recent Work ◽  
Stability Condition ◽  
Digital Filters ◽  
External Interference ◽  
State Delay ◽  
Special Cases ◽  
Saturation Arithmetic ◽  
Asymptotic Stability Condition

This paper presents passivity-based results to address stability of interfered digital filters with state-delay and saturation nonlinearities. A very-strict passivity condition is proposed for the digital filters by using an appropriate Lyapunov-Krasovskii functional. The established criterion ensures limit-cycle free realization of state-delayed interfered digital filters using saturation arithmetic. Conditions for passivity, input-strict passivity and output-strict passivity of the digital filters are obtained as special cases of the proposed result. In addition, an asymptotic stability condition for the digital filters with zero external interference is presented. It is also demonstrated that a stability condition reported in a recent work may be recovered from the established criterion. Numerical simulations are given to demonstrate worthiness of the proposed results.

An improved criterion for peak-to-peak realization of direct-form interfered digital filters employing saturation nonlinearities

2015 ◽  
Vol 34 (3) ◽  
pp. 996-1010 ◽  
Author(s):  
Priyanka Kokil ◽  
Swapnil Sadashiv Shinde
Keyword(s):  
Asymptotic Stability ◽  
State Space ◽  
Digital Filters ◽  
Practical Importance ◽  
External Interference ◽  
Content Type ◽  
Discrete Signals ◽  
Attenuation Level ◽  
Direct Form ◽  
Saturation Arithmetic

Purpose – The purpose of this paper is to present a criterion for global asymptotic stability of state-space direct-form digital filters employing saturation arithmetic. Design/methodology/approach – An elegant use of induced l ∞ approach (also known as a peak-to-peak approach) is made to develop a criterion for the overflow stability of state-space direct-form digital filters. Findings – The criterion not only guarantees asymptotic stability but also reduces the effect of external interference. The presented method yields better interference attenuation level as compared to a recently reported method. Numerical examples are given to illustrate the effectiveness of the proposed method. Practical implications – Digital filters are important dynamical systems in signal processing which are used for the processing of discrete signals. During the implementation of higher-order digital filter in hardware or software, introduction of external interference is unavoidable. Therefore, stability analysis of digital filters in the presence of external interference is of much practical importance. Originality/value – The main result of the paper is reported for the first time and it is useful to establish the asymptotic stability of digital filters in the presence of external disturbances.

scholarly journals An asymptotic stability condition for inhomogeneous simple shear

1989 ◽  
Vol 47 (2) ◽  
pp. 247-262 ◽  
Author(s):  
H. Tz. Chen ◽  
A. S. Douglas ◽  
R. Malek-Madani
Keyword(s):  
Asymptotic Stability ◽  
Simple Shear ◽  
Stability Condition ◽  
Asymptotic Stability Condition
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