169,658 research outputs found
Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method
The paper investigates the exponential stability of a linear system of difference equations with variable delays xk+1=Axk+âi=1sBikxk-mik, k=0,1,âŠâ, where sâN, A is a constant square matrix, Bik are square matrices, mikâNâȘ0, and mikâ€m for an mâN. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed
Sufficient conditions for the exponential stability of delay difference equations with linear parts defined by permutable matrices
This paper deals with the stability problem of nonlinear delay difference equations with linear parts defined by permutable matrices. Several criteria for exponential stability of systems with different types of nonlinearities are proved. Finally, a stability result for a model of population dynamics is proved by applying one of them
Stability and leptogenesis in the left-right symmetric seesaw mechanism
We analyze the left-right symmetric type I+II seesaw mechanism, where an
eight-fold degeneracy among the mass matrices of heavy right-handed neutrinos
M_R is known to exist. Using the stability property of the solutions and their
ability to lead to successful baryogenesis via leptogenesis as additional
criteria, we discriminate among these eight solutions and partially lift their
eight-fold degeneracy. In particular, we find that viable leptogenesis is
generically possible for four out of the eight solutions.Comment: 25 pages, 11 figures, latex; minor changes, published versio
Delay-Independent Stability Analysis of Linear Time-Delay Systems Based on Frequency
This paper studies strong delay-independent stability of linear time-invariant systems. It is known that delay-independent stability of time-delay systems is equivalent to some frequency-dependent linear matrix inequalities. To reduce or eliminate conservatism of stability criteria, the frequency domain is discretized into several sub-intervals, and piecewise constant Lyapunov matrices are employed to analyze the frequency-dependent stability condition. Applying the generalized KalmanâYakubovichâPopov lemma, new necessary and sufficient criteria are then obtained for strong delay-independent stability of systems with a single delay. The effectiveness of the proposed method is illustrated by a numerical example
Discussion for H
Nonsingular H-matrices and positive stable matrices play an important role in the stability of neural network system. In this paper, some criteria for nonsingular H-matrices are obtained by the theory of diagonally dominant matrices and the obtained result is introduced into identifying the stability of neural networks. So the criteria for nonsingular H-matrices are expanded and their application on neural network system is given. Finally, the effectiveness of the results is illustrated by numerical examples
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