Results 261 to 270 of about 349,354 (286)

On the ultimate boundedness of solutions of ordinary differential equations

Applicable Analysis, 1984
The purpose of this paper is to use two Liapunov functions in order to obtain the boundedness and ultimate boundedness of solutions of differential equations. In doing so we extend the results of Yoshizawa and others who used a single Liapunov function. We apply our results to an example whichcan be interpreted as a forced mechanical system with a time
T. Hara, T. Yoneyama, M. Yabuuchi
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Ultimate Boundedness of the Response of a Drilling Pipe Model

IFAC Proceedings Volumes, 2009
Abstract The drill pipe model described by the wave equation with boundary conditions is reduced through the d'Alembert transformation to a difference equation model and an ultimate bound for the velocity at the bottom of the pipe is obtained. The proposal of an energy function for the distributed model allows to provide an ultimate bound for a ...
Martha Belem Saldivar, Sabine Mondié, Emilia Fridman   +2 more
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Ultimate boundedness and invariant measures of stochastic evolution equations

Stochastic and Stochastics Reports, 1996
This work studies necessary and sufficient conditions for the exponential ultimate boundedness of the solutions of stochastic evolution equations in terms of Lyapunov function. We explicitly construct the Lyapunov function in the linear case and derive sufficient conditions in the non linear case through the first order approximation.
V Mandrekar
exaly   +2 more sources

Uniform boundedness and uniform ultimate boundedness for functional differential equations

Funkcialaj Ekvacioj, 1995
The functional differential equation (1) \(x'= f(t, x_t)\), \(t\geq 0\), \(x\in \mathbb{R}^r\), with \(f\) continuous and locally Lipschitz is considered. The delay is finite. The author introduces the ``uniform boundedness'' and ``uniform ultimate boundedness'' for arbitrary \(t_0\geq 0\). A solution \(x\) of (1) is uniformly bounded at \(t_0\) if \[ \
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Ultimate Boundedness of Stochastic Hopfield Neural Networks

Journal of Convergence Information Technology, 2011
Abstract Hopfield neural networks with nonlinear and delay-type template elements have been extensively studied in past years and found many applications for solving a number of problems in various scientific disciplines. Although ultimate boundedness of several classes of neural networks with constant delays was studied by some researchers, the ...
Li WAN -, Qinghua ZHOU -
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On the global uniform ultimate boundedness of a DCAL-like robot controller

IEEE Transactions on Robotics and Automation, 1992
The authors illustrate how the nonadaptive part of the desired compensation adaptive law (DCAL) is a special case of a class of controllers that can be used to obtain a global stability result for the trajectory following problem for robot manipulators.
Dawson, D. M., Qu, Z.
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Nonlinear ultimate boundedness control and stabilization of a flexible robotic arm

Journal of Robotic Systems, 1992
AbstractWe treat the question of control of an elastic robotic arm of two links. Of course, this approach can be extended to other elastic arms. A nonlinear ultimate boundedness controller (UBC) is synthesized such that in the closed‐loop system the joint angle tracking error is uniformly bounded and tends to a certain small neighborhood of the origin.
P. J. Nathan, Sahjendra N. Singh
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Relation between ultimate boundedness and radially unbounded Liapunov function

Nonlinear Analysis: Theory, Methods & Applications, 1986
The authors improve the theorem in ultimately boundedness of the solutions of ordinary differential equations. The main result is: The equiboundedness holds if there are two Lyapunov functions V(t,x) and W(t,x) such that (i) V(t,x)\(\geq K\) on \([0,\infty)\times R^ n\) for a constant K, (ii) W(t,x)\(\to \infty\) as \(| x| \to \infty\) uniformly in t, (
Hara, T., Yoneyama, T., Saitoh, S., Hirano, M.   +3 more
exaly   +3 more sources

Guaranteed Ultimate Boundedness for a Class of Uncertain Linear Dynamical Systems

IEEE Transactions on Automatic Control, 1978
We consider a class of linear dynamical systems with uncertainty in the system matrix, input matrix, input, and state measurement. Based solely on the knowledge of the uncertainty bounds, we give a measured state feedback control that guarantees uniform boundedness and ultimate boundedness in a certain neighborhood of the zero state.
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On ultimate boundedness of delay synchronization algorithms for semi-passive systems

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010
In this paper we study stability of several delay synchronization algorithms for coupled dynamical systems. Using the framework of semi-passive systems, and under appropriate assumptions on the storage function, it is demonstrated that interconnection of control affine nonlinear systems using output or mean field coupling lead to bounded closed loop ...
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