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921.
The problem of stabilizing a second-order SISO LTI system of the form , y=Cx with feedback of the form u(x)=v(x)Cx is considered, where v(x) is real-valued and has domain which is all of . It is shown that, when stabilization is possible, v(x) can be chosen to take on no more than two values throughout the entire state-space (i.e., v(x){k1,k2} for all x and for some k1,k2), and an algorithm for finding a specific choice of v(x) is presented. It is also shown that the classical root locus of the corresponding transfer function C(sI-A)-1B has a strong connection to this stabilization problem, and its utility is demonstrated through examples. 相似文献
922.
923.
924.
925.
In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results. 相似文献
926.
By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solutions for recurrent neural networks with impulsive perturbations and delays. Further, by using numerical simulation method, the influences of the impulsive perturbations on the inherent oscillations are investigated. 相似文献
927.
Colin B. Macdonald Sigal Gottlieb Steven J. Ruuth 《Journal of scientific computing》2008,36(1):89-112
Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer
both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not
possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability
preserving (SSP) time-stepping community which is generally concerned with computing oscillation-free numerical solutions
of PDEs. Using a variety of numerical test problems, we show that although second- and third-order unconditionally contractive
DSRK methods do preserve the strong stability property for all time step-sizes, they suffer from order reduction at large
step-sizes. Indeed, for time-steps larger than those typically chosen for explicit methods, these DSRK methods behave like
first-order implicit methods. This is unfortunate, because it is precisely to allow a large time-step that we choose to use
implicit methods. These results suggest that unconditionally contractive DSRK methods are limited in usefulness as they are
unable to compete with either the first-order backward Euler method for large step-sizes or with Crank–Nicolson or high-order
explicit SSP Runge–Kutta methods for smaller step-sizes.
We also present stage order conditions for DSRK methods and show that the observed order reduction is associated with the
necessarily low stage order of the unconditionally contractive DSRK methods.
The work of C.B. Macdonald was partially supported by an NSERC Canada PGS-D scholarship, a grant from NSERC Canada, and a
scholarship from the Pacific Institute for the Mathematical Sciences (PIMS).
The work of S. Gottlieb was supported by AFOSR grant number FA9550-06-1-0255.
The work of S.J. Ruuth was partially supported by a grant from NSERC Canada. 相似文献
928.
This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given. 相似文献
929.
In this paper, by using the concept of (A,η)-accretive mappings and the new resolvent operator technique associated with (A,η)-accretive mappings, we introduce and study a system of general mixed quasivariational inclusions involving (A,η)-accretive mappings in Banach spaces, and construct a new perturbed iterative algorithm with mixed errors for this system of nonlinear (A,η)-accretive variational inclusions in q-uniformly smooth Banach spaces. Our results improve and generalize the corresponding results of recent works. 相似文献
930.
This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general
dynamical systems described by retarded functional differential and difference equations. Both internal and external stability
properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output
stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization.
In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly,
sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of
coupled systems comprised of retarded functional differential and difference equations. 相似文献