Robust Stabilization for a Class of Uncertain Nonlinear Systems via a Novel Hybrid Control Applicable to Mechanical Systems

Abstract

An important consideration in control system design is that of model uncertainty. Besides, systems with mixed uncertainties, chaotic vibrations, and input nonlinearities are not easily stabilized and traditional control schemes for linear systems are not always effective. Therefore, in this paper, we will solve two problems, first searching a novel hybrid control methodology to achieve the practical stabilization for uncertain systems with mixed uncertainties and second calculating the guaranteed exponential convergence rate with the convergence radius. The applicability of the main results is demonstrated by a tracking controller design for a class of uncertain nonlinear mass-damper-spring systems with mixed uncertainties, chaotic vibrations, and input nonlinearities.

Archives of Control Sciences

“…Stability of a system can be investigated via the first linearization method, but in general and the most powerful technique is the second direct method. For this method one usually assumes the existence of the so called Lyapunov function which is a positive definite function with negative derivative along the trajectories of the system motivated by some earlier works (see [4,9,16,[18][19][20]). Another important problem is to estimate the region of attraction around the equilibrium, that is, the problem of finding a set which contains the origin such that the limit of every trajectory starting inside is the equilibrium point.…”