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.

An Improved Criterion for Induced Stability of Fixed-Point Digital Filters with Saturation Arithmetic

2016 ◽  
Vol 4 (1) ◽  
pp. 65 ◽  
Author(s):  
Priyanka Kokil ◽  
Xavier Arockiaraj S
Keyword(s):  
Fixed Point ◽  
Linear Matrix Inequality ◽  
State Space ◽  
Digital Filters ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
External Interference ◽  
Numerical Examples ◽  
Criterion A ◽  
Saturation Arithmetic

<p>This paper establishes a criterion for the induced  stability of fixed-point state-space digital filters with saturation nonlinearities and external interference. The criterion is established in a linear matrix inequality (LMI) setting, and therefore, computationally tractable. The criterion turns out to be an improvement over a previously reported criterion. A comparison of the presented criterion with existing criterion is made. Numerical examples are given to demonstrate the usefulness of the proposed approach.</p>

New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

2018 ◽  
Vol 40 (15) ◽  
pp. 4246-4252 ◽  
Author(s):  
CG Parthipan ◽  
Xavier S Arockiaraj ◽  
Priyanka Kokil
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
State Space ◽  
Digital Filters ◽  
Linear Matrix ◽  
Input State ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
External Interference ◽  
Simulation Results

This paper considers the passivity performance analysis of fixed-point state-space digital filters with saturation nonlinearities in the presence of external interference. The purpose is to establish new stability criteria in terms of linear matrix inequality (LMI) such that fixed-point state-space digital filters with saturation nonlinearities in the existence of external interference ensure passivity performance with its storage function. The presented results not only ensure state strict and input state strict passivity in the presence of external interference but also confirm asymptotic stability without external interference. The obtained conditions for fixed-point state-space digital filters are based on passivity properties and, hence, are quite novel to previously proposed criteria. Finally, simulation results are given to demonstrate the effectiveness of the proposed work.

Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference

2018 ◽  
Vol 41 (1) ◽  
pp. 156-164 ◽  
Author(s):  
Mani Kant Kumar ◽  
Priyanka Kokil ◽  
Haranath Kar
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Linear Matrix Inequality ◽  
State Space ◽  
Digital Filters ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
External Interference ◽  
Simulation Results

Sufficient criteria for input-to-state stability (ISS) of fixed-point state-space interfered digital filters with generalized overflow non-linearities are presented. The generalized overflow non-linearities under consideration cover the usual types of overflow arithmetic employed in practice, such as saturation, zeroing, two’s complement and triangular. The criteria not only ensure diminishing consequence of external interference but also confirm the asymptotic stability of the system when external interference disappears. The criteria are derived in the linear matrix inequality (LMI) framework. Simulation results are provided to illustrate the utility of the presented approach. With the help of one example, it is illustrated that the presented approach can lead to a less stringent ISS condition for the digital filters with saturation non-linearities compared with a previously reported approach.

Criterion for the limit cycle free state-space digital filters with external disturbances and quantization/overflow nonlinearities

2016 ◽  
Vol 33 (1) ◽  
pp. 64-73 ◽  
Author(s):  
Diksha ◽  
Priyanka Kokil ◽  
Haranath Kar
Keyword(s):  
Exponential Stability ◽  
State Space ◽  
Digital Filters ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
External Interference ◽  
Content Type ◽  
Practical Applications ◽  
Analysis And Synthesis ◽  
The Stability

Purpose – The purpose of this paper is to develop a new criterion for the exponential stability and H ∞ performance of state-space digital filters under the influence of any combination of quantization/overflow nonlinearities. Design/methodology/approach – The proposed criterion uses the H ∞ approach that is suitable for the design of discrete system in the presence of external disturbance. Analysis and synthesis in an H ∞ setting is advantageous as it proposes effective disturbance attenuation, less sensitivity to uncertainties and many practical applications. Findings – The criterion not only guarantees exponential stability but also reduces the effect of external interference. A numerical example demonstrating the effectiveness of the proposed method is given. Originality/value – The main result of the paper is reported for the first time and it is useful to ensure the stability of digital filters in the presence of external disturbance and any combination of quantization/overflow nonlinearities.

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

2019 ◽  
Vol 42 (2) ◽  
pp. 188-197
Author(s):  
CG Parthipan ◽  
Priyanka Kokil
Keyword(s):  
Exponential Stability ◽  
Digital Filters ◽  
External Disturbance ◽  
Linear Matrix ◽  
External Interference ◽  
Attenuation Level ◽  
Simultaneous Existence ◽  
Saturation Arithmetic ◽  
Special Case

This paper presents a sufficient condition for exponential stability and confirms [Formula: see text] performance of state-delayed digital filters in the simultaneous existence of saturation arithmetic and external disturbance. The realization of limit-cycle free state-space digital filters is carried out by utilizing better characterization of saturation nonlinearities. The presented criterion not only ensures exponential stability but also reduces effect of external interference to a specific attenuation level. The obtained condition is in linear matrix inequality framework, so it is easily tractable. It is also shown that many results reported in literature may be retrieved as a special case from the proposed condition. With the help of numerical examples, it is shown that the presented approach provides enhanced stability region for the digital filters as compared to an existing criterion appeared in literature.

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.

Sign in / Sign up

Export Citation Format

Share Document