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A-Stability and Stochastic Mean-Square Stability [PDF]

BIT Numerical Mathematics, 2000
The author considers the mean-square stability of the stochastic differential equation for the test problem with multiplicative noise proposed by \textit{Y. Saito} and \textit{T. Mitsui} [SIAM J. Appl. Math. 56, No. 5, 1400-1423 (1996; Zbl 0869.60053)]. It quantifies precisely the point where unconditional stability is lost.
Burrage, K., Piskarev, S., Higham, D.J.
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Stabilization and pseudo-stabilization

Distributed Computing, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
James E. Burns, Mohamed G. Gouda, Raymond E. Miller   +2 more
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Practical stability and stabilization

IEEE Transactions on Automatic Control, 2000
Summary: We present a practical stability result for dynamical systems depending on a small parameter. This result is applied to a practical stability analysis of fast time-varying systems studied in averaging theory, and of highly oscillatory systems studied by Sussmann and Liu.
Luc Moreau 0002, Dirk Aeyels
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Stability and Stabilization

2016
This chapter is concerned with the stability and stabilization problems of a class of continuous-time and discrete-time Markov jump linear system (MJLS) with partially unknown transition probabilities (TPs). It will be proved that the system under consideration is more general, which covers the systems with completely known and completely unknown TPs ...
Lixian Zhang, Yanzheng Zhu, Peng Shi, Qiugang Lu   +3 more
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Stability and Stabilization

2011
Stability is a fundamental property for dynamic systems. In most engineering projects unstable systems are useless. Therefore in system analysis and control design the stability and stabilization become the first priority to be consider. This chapter considers the stability of dynamic systems and the stabilization and stabilizer design of nonlinear ...
Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
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Finite time stability and stabilization

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
In this paper, finite time stability and stabilization are investigated for systems described by ordinary differential equations (ODE) or differential inclusions: some sufficient conditions are given for scalar and n-dimensional cases. Then, a stabilization result for I/O linearizable systems is derived from these results.
Wilfried Perruquetti, Sergey V. Drakunov
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Semidefinite lyapunov functions stability and stabilization

Mathematics of Control, Signals, and Systems, 1996
The paper gives some weakening of the basic Lyapunov theorems by obtaining stability and asymptotic stability for nonnegatively definite Lyapunov functions. These results allow simpler proofs for some previously known results and some extension of the stabilization results for systems that are affine in the control.
Iggidr, Abderrahman, Kalitine, Boris, Outbib, Rachid   +2 more
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The equivalence ofB-stability andA-stability

BIT, 1984
It is well known that linear and nonlinear stability concepts are equivalent for linear multistep methods in their one-leg formulation. This result is extended to Runge-Kutta methods. In particular, it is shown here that given an irreducible rational function R(z) whose degrees of numerator and denominator are at most s which has order of approximation
Hairer, Ernst, Tuerke, H.
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Arithmetic tests forA-stability,A[α]-stability, and stiff-stability

BIT, 1978
Arithmetic tests forA-stability,A[α]-stability, and stiff-stability are presented as special cases of a general stability test for numerical integration methods. The test evolves from extracted properties of the characteristic polynomial (in two variables) of the numerical method applied to the prototype scalar ordinary differential equation
Bickart, T. A., Jury, E. I.
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Stability and stabilization of implicit systems

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002
This paper is concerned with stability and stabilization of implicit systems. Stability criteria are provided in terms of the Kronecker form, Lyapunov equation and inequality and conditions on extended rank and invertibility of the system pencil. Then stabilization of implicit systems via interconnection is considered based on the notion of initial ...
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