Boundedness properties for time-varying nonlinear systems

• AUTHORS: J. Peuteman, D. Aeyels, R. Sepulchre.
• ABSTRACT: A Lyapunov theorem guaranteeing uniform boundedness and uniform ultimate boundedness for time-varying nonlinear systems is established. The study of these properties for particular classes of time-varying equations $\dot x(t)=f(x(t),t)$ is reduced to the study of the corresponding frozen systems $\dot x(t)=f(x(t),\sigma)$ for all real value of the parameter $sigma $. This approach is illustrated for time-varying homogeneous systems of positive order and for particular classes of non-homogeneous systems including Lotka-Volterra equations.
• KEYWORDS: ordinary differential equations, Lyapunov stability, ultimate boundedness.
• STATUS: SIAM Journal of Control and Optimization, Vol. 39 (5), pp. 1408-1422, 2000.

• Paper: PS file.