Results 21 to 30 of about 282 (64)

New approach to asymptotic stability: time‐varying nonlinear systems

International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 347-366, 1997., 1995
The results of the paper concern a broad family of time‐varying nonlinear systems with differentiable motions. The solutions are established in a form of the necessary and sufficient conditions for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system Lyapunov function and 3) for an accurate single ...
L. T. Grujić
wiley   +1 more source

Razumikhin′s method in the qualitative theory of processes with delay

International Journal of Stochastic Analysis, Volume 8, Issue 3, Page 233-247, 1995., 1995
B.S. Razumikhin′s concept in the qualitative theory of systems delay is clarified and discussed. Various ways of improvements of stability conditions are considered. The author shows that the guiding role of Lyapunov functions and demonstrates Razumikhin′s method as a practical case of continuous version of the mathematical induction.
Anatoly D. Myshkis
wiley   +1 more source

Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 103-112, 1994., 1993
Time‐invariant nonlinear systems with differentiable motions are considered. The algorithmic necessary and sufficient conditions are established in various forms for one‐shot construction of a Lyapunov function, for asymptotic stability of a compact invariant set and for the exact determination of the asymptotic stability domain of the invariant set ...
Ljubomir T. Grujic
wiley   +1 more source

Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 587-596, 1994., 1992
The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o‐uniquely bounded sets, which
Ljubomir T. Grujić
wiley   +1 more source

Global exponential stability and Input-to-State Stability of semilinear hyperbolic systems for the $L^{2}$ norm [PDF]

arXiv, 2020
In this paper we study the global exponential stability in the $L^{2}$ norm of semilinear $1$-$d$ hyperbolic systems on a bounded domain, when the source term and the nonlinear boundary conditions are Lipschitz. We exhibit two sufficient stability conditions: an internal condition and a boundary condition. This result holds also when the source term is
arxiv  

Modeling and sensitivity analysis of HBV epidemic model with convex incidence rate

Results in Physics, 2021
In this article, we study the qualitative analysis of the Hepatitis B epidemic model with convex incidence rate. First, we formulate the model without control and study local and global stability.
Amir Khan, Rahat Zarin, Ghulam Hussain, Auwalu Hamisu Usman, Usa Wannasingha Humphries, J.F. Gomez-Aguilar   +5 more
doaj  

Neural network quaternion-based controller for port-Hamiltonian system

Demonstratio Mathematica
In this research article, a control approach for port-Hamiltonian PH systems based in a neural network (NN) quaternion-based control strategy is presented. First, the dynamics is converted by the implementation of a Poisson bracket in order to facilitate
Alsaadi Fawaz E., Serrano Fernando E., Batrancea Larissa M.   +2 more
doaj   +1 more source

Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold

Advances in Nonlinear Analysis, 2018
Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval [0,2⁢π⁢7/3]{[0,2\pi\sqrt{7/3}]}.
Tang Shuxia, Chu Jixun, Shang Peipei, Coron Jean-Michel   +3 more
doaj   +1 more source

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

Demonstratio Mathematica
In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory.
Choucha Abdelbaki, Boulaaras Salah, Jan Rashid, Alnegga Mohammad   +3 more
doaj   +1 more source

Robustness of Strong Stability of Discrete Semigroups [PDF]

Systems & Control Letters, 75:35--40, 2015, 2014
In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded finite rank perturbations. As the main result we characterize classes of perturbations preserving the strong stability of the semigroup.
arxiv   +1 more source