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On the Stability of Positive Difference Equations
IFAC Proceedings Volumes, 2009In this chapter, we are interested with stability of linear continuous-time difference equations. These equations involve delays, which can be non commensurable. Spectrum analysis comes down to the zeros analysis of an exponential polynomial. From previous results on stability dependent or independent of delays, we focus on the particular case of ...
Di Loreto, Michaël +1 more
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Stability of Volterra Difference Equations
Differential Equations, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kolmanovskii, V. B., Kosareva, N. P.
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Nonuniform Stability of Arbitrary Difference Equations
Results in Mathematics, 2015We describe two approaches to study the robustness of the exponential stability of an arbitrary difference equation with finite delay on a Banach space. The first approach is based on a characterization of Perron-type of the exponential stability in terms of the invertibility of a certain linear operator between spaces of bounded sequences.
Barreira, Luis +2 more
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STABILITY RADII FOR IMPLICIT DIFFERENCE EQUATIONS
Asian-European Journal of Mathematics, 2009This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the l p -real and complex stability radii of these systems coincide and they are given ...
Rodjanadid, Benjawan +3 more
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On Converses to the Stability Theorems for Difference Equations
SIAM Journal on Control, 1972In this paper, converses to a number of the Lyapunov-type stability theorems for difference equations are obtained. The basic vector difference equation considered is \[(1)\qquad X(n + 1) = f(n,X(n))\] subject to the initial condition $X(n_0 ) = x_0$. It is first shown that if the equilibrium $X = 0$ of the difference equation (1) is ...
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A Stability Theory for Perturbed Difference Equations
SIAM Journal on Control, 1972The problem of preserving stability properties under small perturbations for the solutions of difference equations is considered. The approach used is to study the behavior of the solutions of the perturbed difference equation with respect to the solutions of the original unperturbed difference equations. This leads to the introduction of notions which
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On \(\phi_{0}\)-stability of difference equations
Appl. Math. Lett., 2005The authors investigate the comparison difference system \[ x(k+1)=f(k,x(k)),\quad x(k_0)=x_0, \] where \(x\in {\mathbb R}^{\mathbb N}\), \(f\) is a continuous function from \({\mathbb N}_+\times{\mathbb R}^{\mathbb N}\) into \({\mathbb R}^{\mathbb N}\) with \(f(t,0) = 0\), and \({\mathbb N}_+\) is the set of nonnegative integers.
Peiguang Wang, Fengjie Geng
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Robust Stabilizing Solution of the Riccati Difference Equation
European Journal of Control, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianping Zou, Yash P. Gupta
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Global stability of a difference equation with maximum
Applied Mathematics and Computation, 2009The main results of the paper are the following two theorems. Theorem 1. Every positive solution to the difference equation \[ x_n=\max \left \{\frac{1}{x_{n-1}^{\alpha_1}}, \frac{1}{x_{n-2}^{\alpha_2}}, \ldots, \frac{1}{x_{n-k}^{\alpha_k}}\right \}, \qquad n\in \mathbb{N}_0, \] where \(k\in \mathbb{N}\), \(\alpha_i>0\), \(i=1\), \(\ldots\), \(k\) and \
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A note on stability of functional difference equations
Automatica, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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