A universal method for robust stabilization of nonlinear systems: unification and extension of smooth and non-smooth approaches

Abstract

The current literature on the stabilization of nonlinear systems, particularly those whose linearization about the origin may contain uncontrollable modes, essentially contains two distinct methods: a smooth controller scheme (only under strict assumptions) and a non-smooth one. This paper introduces a more general setting under which: 1) unification of the two aforementioned schemes is achieved and 2) it is possible to find a continuously differentiable control law for some systems previously only stabilizable by a continuous controller. This new method is implicitly based on the ideas of homogeneous systems theory and the adding a power integrator technique.

Practical output tracking for a class of uncertain nonlinear time-delay systems via state feedback

“…To the best of our knowlege, many interesting output tracking control problems for time delay inherently nonlinear systems unsolved yet. In this paper, we deal with such as the tracking problems via state feedback domination method in [17,18].…”

“…Using SIMILAR the approach in [11,[17][18], we can design a homogeneous state feedback stabilizer for (8), which can be described in the following Theorem1.…”

Global Practical Output Tracking of Inherently Nonlinear Systems Using Continuously Differentiable Controllers

“…Next, we will present several useful lemmas borrowed from [4,13,14,19], which will play an important role in our later controller design.…”

“…The global stabilization problem of system (1) for > 0 (not restricted to be larger than or equal to one) has been 2 Mathematical Problems in Engineering studied for nonlinear systems in [13,14]. In [13], a continuous controller under a certain nonlinear growth condition is studied.…”

“…The techniques from [11,14] were recently extended in [10,15] to the practical output tracking problem for nonlinear systems (1) by a continuous state feedback controller. However, from the practical point of view, the smoothness of the controllers is always desired because controllers at least 1 avoid the infinity controller gains around the origin and guarantee the uniqueness of the solution [16,17].…”