New Results on Finite-Time Stability: Geometric Conditions and Finite-Time Controllers

This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers based on vector fields and barrier functions to demonstrate the utility of this geometric condition. We also consider the general class of linear controllable systems, and present a continuous feedback control law to stabilize the system in finite time. Finally, we present simulation results for each of these cases, showing the efficacy of the designed control laws.Comment: 2018 American Control Conference, Milwaukee, Wisconsin, June 201

Homogeneous Observer Design for Linear MIMO Systems

International audienceThe paper is devoted to the problem of state observation (particularly, in finite time) of linear MIMO systems. The presented nonlinear observer does not require system transformation to a canonical form and guarantees finite-time (asymptotic with a fixed-time attraction of any compact set containing the origin) stability of observation error equation if homogeneity degree is negative (positive). The proposed observer is robust in input-to-state sense with respect to disturbances and measurement noises. Performance of the observer is illustrated by a numerical example

On State-dependent Discretization of Stable Homogeneous Systems

International audienceConditions for the existence and convergence to zero of numeric approximations with state-depend step of discretization to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time, but in an infinite number of discretization iterations. It is proven that the absolute and relative errors of the respective discretizations are globally bounded functions. Efficiency of the proposed discretization algorithms is demonstrated by the simulation of the super-twisting system

A high-gain-based global finite-time nonlinear observer

In this paper, a global finite-time observer is designed for a class of nonlinear systems with bounded rational powers imposed on the incremental nonlinearities. Compared with the previous global finite-time results, the new observer designed here is with a new gain update law. Moreover, an example is given to show that the proposed observer can reduce the time of the observation error convergence.National Science Foundation of China (Nos. 61074091, 61174216 and 51177088), the National Science Foundation of Hubei Province (2010CDB10807, 2011CDB187) and the Scientific Innovation Team Project of Hubei Provincial Department of Education (T200809, T201103).http://www.tandfonline.com/loi/tcon20hb201

On Finite-Time Robust Stabilization via Nonlinear State Feedback

International audienceA nonlinear control law is designed for finite-time stabilization of a chain of integrators. The method is based on Implicit Lyapunov Function (ILF) technique and homogeneity properties. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The method is simple in implementation and does not assume on-line procedure for computation of the ILF value at the current state that is an improvement with respect to [9], [13]. The control law is presented in an explicit form and allows to find the values of all control parameters, that make the solution one of the most constructive. The theoretical results are supported by numerical example

Robust finite-time output feedback stabilization of the double integrator

International audienceThe problem of finite-time output stabilization of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilization. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretization on the obtained closed loop system are analyzed. The efficiency of the obtained solution is demonstrated in computer simulations

Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control

This paper addresses the problem of finite-time synchronization for a class of multi-layer nonlinear coupled complex networks via intermittent feedback control. Firstly, based on finite-time stability theory, some novel criteria are given to guarantee that the error system of drive-response systems is still finite-time stable under an inherently discontinuous controller. Then, by proposing two kinds of intermittent feedback control laws, sufficient conditions of finite-time synchronization of two kinds of multi-layer complex networks are derived, respectively. The time delay between different layers is also taken into consideration. Finally, a numerical example is provided to verify the effectiveness of the proposed methods.http://www.elsevier.com/locate/neucom2018-02-28hb2017Electrical, Electronic and Computer Engineerin

Globally uniformly ultimately bounded observer design for a class of nonlinear systems with sampled and delayed measurements

In this paper, we consider two kinds of sampled-data observer design for a class of nonlin- ear systems. The system output is sampled and transmitted under two kinds of truncations. Firstly, we present de nitions of the truncations and the globally uniformly ultimately bounded observer, respectively. Then, two kinds of observers are proposed by using the delayed measure- ments with these two truncations, respectively. The observers are hybrid in essence. For the rst kind of observers, by constructing a Lyapunov{Krasovskii functional, su cient conditions of globally uniformly ultimately bounded of the estimation errors are derived, and the maxi- mum allowable sampling period and the maximum delay are also given. For the second ones, su cient conditions are also given to ensure that the estimation errors are globally uniformly ultimately bounded. Finally, an example is provided to illustrate the design methods.The National Science Foundation of China (61374028), Grant National Science Foundation of Hubei Provincial (2013CFA050), and the Scientific Innovation Team Project of Hubei Provincial Department of Education (T201504).http://dml.cz/dmlcz/145785am2017Electrical, Electronic and Computer Engineerin