On finite‐time robust stabilization via nonlinear state feedback

Abstract

Summary A nonlinear control law is designed for finite‐time stabilization of a chain of integrators. The method is based on the implicit Lyapunov function technique and homogeneity properties. The scheme of control parameter selection is presented by a linear matrix inequality. The method is simple in implementation and does not assume an online procedure for the computation of the implicit Lyapunov function value at the current state that is an improvement with respect to the works of Polyakov et al. The control law is presented in an explicit form and allows finding the values of all control parameters that make the solution one of the most constructive. The theoretical results are supported by numerical examples.

On Homogeneous Descriptor Systems and Homogeneity-Based Finite-Time Control of Linear Descriptor Systems

“…In this case, if the control (16) calculated via Theorem 2 provides settling time estimation (25) greater than the desired transient time, the convergence rate of the proposed control can be accelerated via time rescaling. To accelerate the convergence rate of systems in the form of ODEs with homogeneous control, one can refer to the results [35]- [37]. The following corollary provides an extension of Theorem 2 in order to accelerate the convergence rate.…”

Finite-Time Stability Tools for Control and Estimation

“…The first one is based on a development of an appropriate computational scheme for digital implementation of the proposed controller (see Chapter 6). An alternative approach was introduced for the weighted dilation in Zimenko et al, 2018 where • d was replaced with an explicitly defined homogeneous norm. For linear geometric dilation the suggested scheme is formalized by the following proposition.…”

Finite-time control for systems with multiple disturbances based on adaptive disturbance observer

“…Meanwhile, the finite-time control has attracted much attention because of its fast transient response, strong robustness and finite-time convergence. 22–27 In the work by Pukdeboon et al, 28 the external disturbances and parameter uncertainties were regarded as a total disturbance, and sliding control-based extended state observer technique was proposed to ensure the finite-time convergence of the system. In the work by Gu et al, 29 a finite-time H ∞ adaptive control strategy was presented for linear systems with unknown mismatched perturbation, which guaranteed the finite-time bounded of the system.…”