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Spectral Test for the Exponential Stability
Differential Equations, 2021Consider the \(n\)-th order differential equation \[ A_{0}X^{(n)} +A_{1}X^{(n-1)}+\dots+A_{n-1}\dot{X}+A_{n}X=0, \tag{1} \] where \(A_{0},A_{1},\dots,A_{n}\) are constant \(m\times m\) matrices, the matrix \(A_{0}\) is nonsingular and \(X^{(k)}= \frac{d^{k}X}{dt^{k}}\), \(0 \leq k \leq n\). Let \(S(A)\) denote the spectrum of a matrix \(A\).
Perov, A. I., Kostrub, I. D.
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Spectral Test for Exponential Stability
Mathematical Notes, 2023In this paper, the authors first consider an nth-order linear differential equation with constant coefficients in the complex Banach algebra B. Next, they also consider a linear system of ordinary differential equations with constant coefficients. Using the theory of commutative Banach algebras, an estimate of the solution with regard to the nth-order ...
Kostrub, I. D., Perov, A. I.
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Exponential Stability With RISE Controllers
IEEE Control Systems Letters, 2022A class of continuous robust controllers termed Robust Integral of the Sign of the Error (RISE) have been published over the past two decades as a means to yield asymptotic tracking error convergence and asymptotic identification of time-varying uncertainties, for classes of nonlinear systems that are subject to sufficiently smooth bounded exogenous ...
Omkar Sudhir Patil +3 more
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Exponential stability and stabilization of nD systems
2015 54th IEEE Conference on Decision and Control (CDC), 2015The paper considers nonlinear nD discrete and continuous systems described by a state-space model of the Roesser form where the property of exponential stability is characterized by use of a vector Lyapunov function. The property of exponential dissipativity is defined and a particular case of this property, termed exponential passivity, is used ...
Pavel V. Pakshin +3 more
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Stability for Multivariate Exponential Families
Journal of Mathematical Sciences, 2001Let \(E\) be a Euclidean space, let \(Z :\Omega\to E\) be a nondegenerate random vector, and suppose there is an open convex set \(D\subset E\) such that \(P(Z\in \overline{D}) = 1\). If \(\mu\) is the distribution of \(Z\), define measures \(\mu_\lambda\) by \(d\mu_\lambda(x) = e^{\lambda x}d\mu(x)\), \(x\in E\), for any \(\lambda\) in the dual space \
Balkema, A. A. +2 more
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Almost exponential stability and exponential stability of resolvent operator families
Semigroup Forum, 2016A new concept of almost exponential stability of the resolvent operator family \(\{ R(t), \, t\geq 0 \},\) \[ R(t) x = x+ \int_0^t a(t-\tau) A R(\tau) x\,d\tau, \, x\in {\mathcal D}(A),\quad A: {\mathcal D}(A ) \subseteq X\rightarrow X \] is constructed.
Fan, Zhenbin, Dong, Qixiang, Li, Gang
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Estimate of Exponential Convergence Rate and Exponential Stability for Neural Networks [PDF]
IEEE Transactions on Neural Networks, 1999 Estimate of exponential convergence rate and exponential stability are studied for a class of neural networks which includes the Hopfield neural networks and the cellular neural networks. Both local and global exponential convergence is discussed.
Zhang Yi, P A Heng
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Stability of binary exponential backoff
Journal of the ACM, 1988Binary exponential backoff is a randomized protocol for regulating transmissions on a multiple-access broadcast channel. Ethernet, a local-area network, is built upon this protocol. The fundamental theoretical issue is stability: Does the backlog of packets awaiting transmission remain bounded in time, provided the rates of new packet arrivals are ...
Jonathan Goodman +3 more
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Exponential growth bound and exponential stability
1998In Section 5.1, we characterize the exponential growth bound of the propagators of (ACP n ) in a Hilbert space in terms of the behavior of on vertical lines in a half complex plane. As a consequence we show that the propagators are exponentially stable if P λ is boundedly invertible in {λ ∈ C; Reλ ≥ 0} with uniformly bounded there.
Ti-Jun Xiao, Jin Liang
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On the Exponential Stability of Discrete Semigroups
Qualitative Theory of Dynamical Systems, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zada, Akbar +3 more
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