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The stability of systems with multiplicative feedback

Automatica, 1968
The global phase-portrait concept of Poincare is used initially to predict the stability of two continuous systems which have multiplicative feedback. Singularities at infinity are revealed which are coalitions of saddle points and nodes. Where stability is not global, Lyapunov functions are generated to define the domain of stability in the general ...
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Feedback stability and unsupervised learning

IEEE International Conference on Neural Networks, 1988
Global stability is examined for nonlinear feedback dynamical systems subject to unsupervised learning. Only differentiable neural models are discussed. The unconditional stability of Hebbian learning systems is summarized in the adaptive bidirectional associative memory (ABAM) theorem.
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Output feedback stabilization of a vibrating gyroscope

Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003., 2004
In this paper we give a solution to the output feedback stabilization problem of a vibrating gyroscope. The system is modelled as an interconnected system, and the coupling terms between subsystems are functions of the uncertain rotation speed. The formulation is made in an LMI framework.
Mehdi, Driss   +3 more
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Feedback stabilization, stability and chaotic dynamics

1985 24th IEEE Conference on Decision and Control, 1985
We examine the control of a (prototype) nonlinear pendulum under uncertainty in modelling. The uncertainty is sufficiently small and is a function of both state and time. We apply Liapunov direct method to prove the stability of an equilibrium point.
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Examples of stabilization with hybrid feedback

1996
Via examples, this paper examines the possibility of stabilizing a continuous control plant, through an interaction with a discrete time controller. Such a hybrid feedback complements the output feedback within the plant when the latter fails to stabilize the system or fails to produce smooth stabilization.
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CausalC 0 operators and feedback stability

Mathematical Systems Theory, 1977
Linear feedback systems, for which the return differenceT is aC0 operator are studied. It is shown that ifT is essentially unitary then such a system is well posed and stable. All strictly causalC0 operators for whichI–T*T is compact are characterized.
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On the Synthesis of a Stabilizing Feedback Control

2006
Starting from states near to a closed set S we want to steer S and to stay always close to S. Unfortunately, open-loop controls are very sensitive to disturbances and can lead to very bad practical results. For that reason, we propose an approach for constructing a discontinuous feedback control law that asymptotically stabilizes the system in a ...
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Feedback Stabilization of a Fluid-Structure Model

SIAM Journal on Control and Optimization, 2010
We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular-type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation of the beam, the fluid domain depends on time.
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Stabilization by unbounded and periodic feedback

International Journal of Control, 2022
Makrem Salhi, Farhat Shel
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