This note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable, and an upper bound of the settling-time function can be arbitrarily chosen a priori through a suitable selection of the system parameters. We show that the studied Lyapunov-like conditions allow to demonstrate equivalence between previous Lyapunov theorems for predefined-time stability for autonomous systems. Moreover, the obtained Lyapunov-like theorem is extended for analyzing the property of predefined-time ultimate boundedness with predefined bound, which is useful when analyzing uncertain dynamical systems. Therefore, the proposed results constitute a general framework for analyzing predefinedtime stability, and they also unify a broad class of systems that present the predefined-time stability property. On the other hand, the proposed framework is used to design robust controllers for affine control systems, which induce predefined-time stability (predefined-time ultimate boundedness of the solutions) w.r.t. to some desired manifold. A simulation example is presented to show the behavior of a developed controller, especially regarding the settling time estimation.

This paper deals with the predefined-time stabilization problem for a class of uncertain chained-form nonholonomic systems. Based on a novel generalized Lyapunov-like characterization of predefined-time stability, new predefined-time controllers are introduced for a class of first and second order systems with matched perturbations. Contrary to existing finite-time and fixed-time schemes, an upper bound of the settling time is an easily tunable control parameter. Then, these results for first and second order systems are used to design a switching strategy, which guarantees the predefined-time stability of the closed-loop system. The switching time and the settling-time can be easily tuned according to the control parameters. A benchmark example is presented to show the effectiveness of the proposed method.

Light weight quadrotors are highly manoeuvrable autonomous aerial robots (UAV) that outperform most UAVs; however, quadrotors are prone to a wide class of aerodynamic disturbances, vibrations, and uncertainties that demand not only robust but fast attitude control structures. These arguments are compelling enough to motivate the design of a novel fractional‐order control scheme that enforces finite‐time convergence of the sliding manifold to guarantee local exponential tracking. The controller does not exhibit chattering and does not require the knowledge of the dynamic model. The stability analysis is based on a proposed resetting memory principle to deal with memory effects of the differintegral operator, which allows the controller to tackle also robustness against continuous disturbances that are not necessarily differentiable in the conventional sense such as some aerodynamic phenomena. Experimental evidence is presented and discussed to expose the enforcement of the sliding manifold based on a fractional‐order reaching phase that demonstrates the feasibility of the proposed control scheme.