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.

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>

Novel Results for Induced l∞ Stability for Digital Filters with External Noise

2017 ◽  
Vol 16 (04) ◽  
pp. 1750032 ◽  
Author(s):  
Priyanka Kokil ◽  
S. Xavier Arockiaraj
Keyword(s):  
Fixed Point ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
Digital Filters ◽  
External Noise ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
External Interference ◽  
Overflow Oscillations

This paper establishes novel criteria for the induced [Formula: see text] stability to avoid overflow oscillations in fixed-point digital filters with generalized overflow non-linearities and external noise. The proposed linear matrix inequality (LMI)-based criteria ensure exponential stability as well as confirm reduction in the influence of external noise. The generalized overflow non-linearities which are considered for analysis commonly occur in practice, viz. saturation, zeroing, two's complement, and triangular. The presented approach unifies a string of existing results which are derived by considering saturation non-linearities and external interference. Simulation examples are shown to validate the usefulness of the proposed approach.

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.

LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (03) ◽  
pp. 257-265 ◽  
Author(s):  
TAO LI ◽  
CHANGYIN SUN ◽  
XIANLIN ZHAO ◽  
CHONG LIN
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Activation Functions ◽  
Different Types ◽  
Conservative Result

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

Observer Design for Lipschitz Nonlinear Systems with Output Uncertainty

2014 ◽  
Vol 533 ◽  
pp. 277-280
Author(s):  
Wei Zou ◽  
Yu Sheng Liu ◽  
Kai Liu
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Observer Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Output Uncertainty ◽  
Lipschitz Nonlinear Systems ◽  
Simulation Results

This paper presents an observer design for Lipschitz nonlinear systems with output uncertainty. By means of Lyapunov method as well as linear matrix inequality (LMI), the observer gain matrix is determined and a sufficient condition ensuring the asymptotic stability of the observer is proposed. Simulation results demonstrate the robustness of the proposed observer for output uncertainty.

Sign in / Sign up

Export Citation Format

Share Document