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Sourav Patra - One of the best experts on this subject based on the ideXlab platform.

  • Integral Control of Stable Negative-Imaginary Systems Preceded by Hysteresis Nonlinearity
    IEEE Transactions on Automatic Control, 2020
    Co-Authors: Sourav Patra
    Abstract:

    In this note, constant reference tracking using integral control for negative-imaginary (NI) systems preceded by hysteresis nonlinearity is addressed. The hysteresis nonlinearity is considered to be slope-restricted, though no specific modeling framework is exploited. It is effectively shown that integral tracking controllers are guaranteed to exist when a stable NI system with sign-definite dc-gain is preceded by sauch hysteresis nonlinearities. When the dc-gain is negative-definite, under Positive feedback configuration with Positive slope-restricted hysteresis, it is established that the integral controller gain can be any Positive Diagonal Matrix. The development of the proposed model-independent inversion-free scheme is carried out in general state-space setting and is applicable for multiple-input multiple-output systems with decoupled hysteresis nonlinearities. Effectiveness of the results is illustrated with examples.

  • Absolute stability analysis for negative-imaginary systems
    Automatica, 2016
    Co-Authors: Arnab Dey, Sourav Patra, Siddhartha Sen
    Abstract:

    This paper deals with absolute stability of a Lur'e system with Positive feedback where the linear subsystem exhibits negative-imaginary frequency response and the nonlinearity connected in feedback is time-invariant, memoryless and slope-restricted. The proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative-imaginary class. Along with that, Positive definiteness of a symmetric Matrix needs to be ensured, where the symmetric Matrix is obtained by subtracting the dc-gain Matrix of the linear subsystem from a strictly Positive Diagonal Matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities. The stability criterion is proved using a Lur'e-Postnikov-type Lyapunov function. Numerical examples are presented to demonstrate the proposed results.

Chen Qiao - One of the best experts on this subject based on the ideXlab platform.

  • A critical global convergence analysis of recurrent neural networks with general projection mappings
    Neurocomputing, 2009
    Co-Authors: Chen Qiao
    Abstract:

    In this paper, we present some general analysis on global convergence of the recurrent neural networks (RNNs) with projection mappings in the critical case when M(L,@C), a Matrix related to the weight matrices and the activation mappings of the networks, is nonnegative definite for some Positive Diagonal Matrix @C. Considerable stability results have been obtained for the RNNs in the noncritical case when M(L,@C) is Positive definite. In contrast, only a few conclusions have been conducted under the critical conditions. Comparing with the existing critical studies, the present critical stability results in this paper require no additional assumption on the weight matrices, can be applied to the RNNs with general projection mappings other than nearest point projection mappings, and can serve for both two fundamental RNN models. The results established for several typical RNN models unify, sharpen or generalize most of the existing stability assertions. Two examples are given to show both theoretical importance and practical feasibility of the critical results obtained.

  • ISNN (3) - New Critical Analysis on Global Convergence of Recurrent Neural Networks with Projection Mappings
    Advances in Neural Networks – ISNN 2007, 2007
    Co-Authors: Chen Qiao
    Abstract:

    In this paper, we present the general analysis of global convergence for the recurrent neural networks (RNNs) with projection mappings in the critical case that M(L,Γ), a Matrix related with the weight Matrix Wand the activation mapping of the networks, is nonnegative for a Positive Diagonal Matrix Γ. In contrast to the existing conclusion such as in [1], the present critical stability results do not require the condition that ΓWmust be symmetric and can be applied to the general projection mappings other than nearest point projection mappings. An example has also been shown that the theoretical results obtained in the present paper have explicitly practical application.

N. Chakravarti - One of the best experts on this subject based on the ideXlab platform.

  • AnO(n ^2) active set method for solving a certain parametric quadratic program
    Journal of Optimization Theory and Applications, 1992
    Co-Authors: M. J. Best, N. Chakravarti
    Abstract:

    This paper presents an O ( n ^2) method for solving the parametric quadratic program $$\min (1/2)x'Dx - a'x + (\lambda /2)\left( {\sum\limits_{j = 1}^n {\gamma _j x_j } - c} \right)^2 ,$$ having lower and upper bounds on the variables, for all nonnegative values of the parameter λ. Here, D is a Positive Diagonal Matrix, a an arbitrary n -vecotr, each γ_ j , j =1, ..., n , and c are arbitrary scalars. An application to economics is also presented.

  • An O ( n 2 ) active set method for solving a certain parametric quadratic program
    Journal of Optimization Theory and Applications, 1992
    Co-Authors: M. J. Best, N. Chakravarti
    Abstract:

    This paper presents anO(n 2) method for solving the parametric quadratic program $$\min (1/2)x'Dx - a'x + (\lambda /2)\left( {\sum\limits_{j = 1}^n {\gamma _j x_j } - c} \right)^2 ,$$ having lower and upper bounds on the variables, for all nonnegative values of the parameter λ. Here,D is a Positive Diagonal Matrix,a an arbitraryn-vecotr, each γ j ,j=1, ...,n, andc are arbitrary scalars. An application to economics is also presented.

Li Yang - One of the best experts on this subject based on the ideXlab platform.

  • Local(α,β)-Diagonally Dominant Matrix With a Nonzero Elements Chain
    Journal of Liaoning University of Petroleum & Chemical Technology, 2007
    Co-Authors: Li Yang
    Abstract:

    The concepts of local(α,β)-Diagonally dominant Matrix were introduced.Under the condition of local(α,β)-Diagonally dominant Matrix with a nonzero elements chain,by constructing a Positive Diagonal Matrix X,the conclusion that B=AX was α-Diagonally dominant Matrix with a nonzero elements chain was presented,and a criterion for nonsingular H-Matrix was obtained.The outcome implies that the extended local(α,β)-Diagonally dominant concept is a development for Matrix's Diagonally dominance's theory,and a strong tool for researching H-Matrix and M-Matrix.

  • Two Subsets of Nonsingular H-Matrix
    Journal of Petrochemical Universities, 2006
    Co-Authors: Li Yang
    Abstract:

    The concept of local(α,β)-doubly Diagonally dominant Matrix was introduced.Under the conditions of strict local(α,β)-doubly Diagonally dominant and irreducible local(α,β)-doubly Diagonally dominant Matrix,the conclusion that B=AX is a strict α-Diagonally dominant Matrix or irreducible α-Diagonally dominant Matrix was presented by constructing a suitable Positive Diagonal Matrix X, for a given complex Matrix A,thus two practical criterions of nonsingular HMatrix were obtained.The results show that the extended local (α,β)-doubly Diagonally dominant concept is a development for Matrix's doubly Diagonally dominance's theory and a powerful tool for researching of H-Matrix and M-Matrix.These conclusions not only promote the development of Matrix's theory itself,but also provide strong basis for the research of relative fields such as computational mathematic,control theory,etc.

M. J. Best - One of the best experts on this subject based on the ideXlab platform.

  • AnO(n ^2) active set method for solving a certain parametric quadratic program
    Journal of Optimization Theory and Applications, 1992
    Co-Authors: M. J. Best, N. Chakravarti
    Abstract:

    This paper presents an O ( n ^2) method for solving the parametric quadratic program $$\min (1/2)x'Dx - a'x + (\lambda /2)\left( {\sum\limits_{j = 1}^n {\gamma _j x_j } - c} \right)^2 ,$$ having lower and upper bounds on the variables, for all nonnegative values of the parameter λ. Here, D is a Positive Diagonal Matrix, a an arbitrary n -vecotr, each γ_ j , j =1, ..., n , and c are arbitrary scalars. An application to economics is also presented.

  • An O ( n 2 ) active set method for solving a certain parametric quadratic program
    Journal of Optimization Theory and Applications, 1992
    Co-Authors: M. J. Best, N. Chakravarti
    Abstract:

    This paper presents anO(n 2) method for solving the parametric quadratic program $$\min (1/2)x'Dx - a'x + (\lambda /2)\left( {\sum\limits_{j = 1}^n {\gamma _j x_j } - c} \right)^2 ,$$ having lower and upper bounds on the variables, for all nonnegative values of the parameter λ. Here,D is a Positive Diagonal Matrix,a an arbitraryn-vecotr, each γ j ,j=1, ...,n, andc are arbitrary scalars. An application to economics is also presented.