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Article Citation - WoS: 19Citation - Scopus: 22Improved Lmi-Based Criterion for Global Asymptotic Stability of 2-D State-Space Digital Filters Described by Roesser Model Using Two's Complement Arithmetic(Academic Press inc Elsevier Science, 2012) Singh, VimalAn LMI-based criterion for the global asymptotic stability of 2-D state-space digital filters described by the Roesser model employing two's complement overflow arithmetic is presented. Under a certain assumption, the criterion turns out to be an improvement over a criterion due to El-Agizi and Fahmy pertaining to two's complement arithmetic and has a form similar to a criterion due to Xiao and Hill pertaining to saturation arithmetic. Examples show the effectiveness of the new criterion. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 15Citation - Scopus: 17Improved Global Robust Stability of Interval Delayed Neural Networks Via Split Interval: Generalizations(Elsevier Science inc, 2008) Singh, VimaldThe problem of global robust stability of Hop field-type delayed neural networks with the intervalized network parameters is revisited. Recently, a computationally tractable, i.e., linear matrix inequality (LMI) based global robust stability criterion derived from an earlier criterion based on dividing the given interval into more that two intervals has been presented. In the present paper, generalizations, i.e., division of the given interval into m intervals (where m is an integer greater than or equal to 2) is considered and some new LMI-based global robust stability criteria are derived. It is shown that, in some cases, m = 2 may not suffice, i.e., m > 2 may be needed to realize the improvement. An example showing the effectiveness of the proposed generalization is given. The paper also provides a complete and systematic explanation of the "split interval" idea. (c) 2008 Elsevier Inc. All rights reserved.Article Citation - WoS: 14Citation - Scopus: 15Lmi Approach To the Global Robust Stability of a Larger Class of Neural Networks With Delay(Pergamon-elsevier Science Ltd, 2007) Singh, VimalSufficient conditions in the form of linear matrix inequality for the uniqueness and global asymptotic stability of the equilibrium point of a large class of uncertain neural networks with delay are presented. The conditions are based on norm-bounded uncertainties. An example is given to show the effectiveness of the obtained results. A comparison is made between the present approach and an earlier approach due to Lu, Rong and Chen. An error is corrected in an earlier publication. (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.Article Citation - WoS: 1Citation - Scopus: 1Novel Frequency-Domain Criterion for Elimination of Limit Cycles in a Class of Digital Filters With Single Saturation Nonlinearity(Pergamon-elsevier Science Ltd, 2008) Singh, VimalA frequency-domain criterion for the elimination of limit cycles in a class of digital filters utilizing single saturation nonlinearity is presented. The criterion is derived by exploiting the structural properties of the system under consideration in a greater detail. A novel feature of the criterion is that it takes the form of a matrix inequality, despite the fact that there is single nonlinearity in the system. An example showing the effectiveness of the criterion is given. (c) 2006 Elsevier Ltd. All rights reserved.Article Citation - WoS: 13Citation - Scopus: 12Novel Global Robust Stability Criterion for Neural Networks With Delay(Pergamon-elsevier Science Ltd, 2009) Singh, Vimal; Sıngh, Vımal; Sıngh, Vımal; Department of Mechatronics Engineering; Department of Mechatronics EngineeringA novel criterion for the global robust stability of Hopfield-type interval neural networks with delay is presented. An example illustrating the improvement of the present criterion over several recently reported criteria is given. (C) 2008 Elsevier Ltd. All rights reserved.Article Citation - WoS: 30Citation - Scopus: 30New approach to stability of 2-D discrete systems with state saturation(Elsevier, 2012) Singh, VimalA new criterion for the global asymptotic stability of 2-D discrete systems described by the Roesser model using saturation arithmetic is presented. The criterion is a generalization over an earlier criterion due to Liu and Michel. The generalized criterion has the feature that Lyapunov matrix P is not restricted to be symmetric, i.e., P can be even unsymmetric. A modified form of the criterion is also presented. Two examples showing the effectiveness of the generalized approach to yield new 2-D stability results are provided. To the best of author's knowledge, the use of unsymmetric P to obtain new 2-D stability conditions (i.e., conditions which are outside the scope of symmetric P) is demonstrated, for first time, in this paper. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 14Citation - Scopus: 15Global asymptotic stability of 2-D state-space digital filters with saturation arithmetic: Modified approach(Elsevier Science Bv, 2008) Singh, VimalA criterion for the global asymptotic stability of 2-D state-space digital filters described by the Roesser model employing state saturation arithmetic is presented. The criterion is a modified form of a recently reported criterion. An example shows the effectiveness of the modified criterion. (C) 2007 Elsevier B.V. All rights reserved.Article Citation - WoS: 34Citation - 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.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.
