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Article Citation - WoS: 7Citation - Scopus: 8Some Remarks on Global Asymptotic Stability of Neural Networks With Constant Time Delay(Pergamon-elsevier Science Ltd, 2007) Singh, VimalAn elegant proof of a previously reported criterion for the uniqueness and global asymptotic stability of the equilibrium point of a class of neural networks with constant time delay is presented. The present proof yields some interesting observations. (c) 2005 Elsevier Ltd. All rights reserved.Article Citation - WoS: 18Citation - Scopus: 18Stability Analysis of 2-D Linear Discrete Systems Based on the Fornasini-Marchesini Second Model: Stability With Asymmetric Lyapunov Matrix(Academic Press inc Elsevier Science, 2014) Singh, VimalThe stability of two-dimensional (2-D) linear discrete systems based on the Fornasini-Marchesini local state-space (LSS) model is considered. A stability criterion using the asymmetric Lyapunov matrix P is presented. A special case of the criterion is discussed. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 11Modified Criteria for Global Robust Stability of Interval Delayed Neural Networks(Elsevier Science inc, 2009) Singh, VimalTwo simple criteria for global robust stability of Hopfield-type interval neural networks with delay are presented. The criteria turn out to be modified versions of an earlier criterion due to Cao, Huang, and Qu. Examples show the effectiveness of the modified criteria. Numerical simulations are carried out to confirm the applicability of the modified criteria. (C) 2009 Elsevier Inc. All rights reserved.Article Citation - WoS: 33Citation - Scopus: 38Discussion on Barkhausen and Nyquist Stability Criteria(Springer, 2010) Singh, VimalMost textbooks on analog circuits and signal processing describe the Barkhausen criterion pertaining to the determination of sinusoidal oscillations in a closed-loop system. On the other hand, the Nyquist stability criterion is well known, as discussed in most textbooks on control systems. Recently, some examples in which the Barkhausen criterion fails to produce the correct condition for startup of oscillations have been reported. In the present paper, an explanation of oscillation startup based on the Nyquist stability criterion is given and the close relationship between the Barkhausen and the Nyquist criteria highlighted. It is shown that the Nyquist criterion (which is a rigorous technique) is a more robust approach than the Barkhausen criterion concerning the determination of sinusoidal oscillations in a closed-loop system and that the Barkhausen criterion (whenever it yields the correct result) is subsumed by the Nyquist criterion as a special case. The textbooks usually describe the Barkhausen criterion as a separate topic, i.e., do not discuss the relationship of this criterion with the Nyquist criterion. It is, therefore, felt that the present discussion will go a long way to put the subject in a broader perspective.Letter Citation - WoS: 22Citation - Scopus: 24A Note on Determination of Oscillation Startup Condition(Springer, 2006) Singh, VimalThere prevails a widespread notion that, given a closed-loop system, oscillation will commence and build up therein if the magnitude of loop gain is greater than unity at the frequency at which the angle of loop gain is zero degree. Three novel examples in which this notion fails are presented.Article Citation - WoS: 26Citation - Scopus: 31New Lmi Condition for the Nonexistence of Overflow Oscillations in 2-D State-Space Digital Filters Using Saturation Arithmetic(Academic Press inc Elsevier Science, 2007) Singh, VimalA new criterion for the nonexistence of overflow oscillations in 2-D state-space digital filters described by Roesser model using saturation arithmetic is presented. The criterion is in the form of a linear matrix inequality (LMI) and hence computationally tractable. The criterion is compared with an earlier LMI-based criterion due to Xiao and Hill. It turns out that the present criterion may uncover some new A (i.e., other than those arrived at via Xiao-Hill's criterion) for which the absence of overflow oscillations is assured. (c) 2006 Elsevier Inc. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 14Improved Global Robust Stability for Interval-Delayed Hopfield Neural Networks(Springer, 2008) Singh, VimalA modified form of a recent criterion for the global robust stability of interval-delayed Hopfield neural networks is presented. The effectiveness of the modified criterion is demonstrated with the help of an example.Article Citation - WoS: 5Citation - Scopus: 52-D Digital Filter Realization Without Overflow Oscillations(Pergamon-elsevier Science Ltd, 2013) Singh, VimalA novel criterion for the elimination of overflow oscillations in 2-D state-space digital filters described by the Roesser model employing two's complement overflow arithmetic is presented. The criterion takes the form of linear matrix inequality (LMI) and, hence, is computationally tractable. The criterion is a generalization and improvement over an earlier criterion. An example shows the effectiveness of the new criterion. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 6A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic(Pergamon-elsevier Science Ltd, 2007) Singh, VimalIn [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters. (C) 2006 Elsevier Ltd. All rights reserved.Letter Citation - WoS: 3Citation - Scopus: 3Global Robust Stability of Interval Delayed Neural Networks: Modified Approach(Wiley, 2009) Singh, VimalA criterion for the global robust stability of Hopfield-type delayed neural networks with the intervalized network parameters is presented. The criterion, which is derived by utilizing the idea of splitting the given interval into two intervals, is in the form of linear matrix inequality and, hence, computationally tractable. The criterion yields a less conservative condition compared with many recently reported criteria, as is demonstrated with an example. Copyright (C) 2008 John Wiley & Sons, Ltd.
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