Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Asymptotic stability of nonautonomous systems by Liapunov's direct method
Systems & Control Letters
An averaging theorem for time-periodic degree zero homogeneous differential equations
Systems & Control Letters
Brief paper: Averaging techniques without requiring a fast time-varying differential equation
Automatica (Journal of IFAC)
On the Stabilization of Persistently Excited Linear Systems
SIAM Journal on Control and Optimization
| Hi-index | 22.15 |
Within the Liapunov framework, a sufficient condition for exponential stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the Liapunov function, taken along solutions of the system, may have positive and negative values. Verification of the conditions of the main theorem may be harder than in the classical case. It is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time-varying systems. This sets the stability study by means of averaging in a Liapunov context. In particular, it is established that exponential stability of the averaged system implies exponential stability of the original fast time-varying system. A comparison of our work with results taken from the literature is included.