Global finite‐time stabilization of planar nonlinear systems with disturbance

Robust finite‐time stability and stabilization problems for a class of linear uncertain time‐delay systems are studied. The concept of finite‐time stability is extended to linear uncertain time‐delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite‐time stability of linear uncertain time‐delay systems is given. By virtue of the results on finite‐time stability, a memoryless state feedback controller that guarantees that the closed‐loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Finite‐Time Stability and Stabilization of Linear Uncertain Time‐Delay Systems

Stojanović¹,

Debeljković²,

Antić³

2013

“…• To study the stability analysis of the proposed observer-estimator based on higher sliding mode control ( [32][33][34][35]) in closed loop.…”

Section: Concluding Remarks and Ongoing Workmentioning

confidence: 99%

Observability Analysis and Improved Zero‐Speed Position Observer Design of Synchronous Motor with Experimental Results

Zaltni¹,

Ghanes²

2012

This paper deals with the permanent magnet synchronous motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially towords the necessary observability condition analysis. Furthermore, improved zero-speed observation is presented here for a surface PMSM (SPMSM) to overcome position observability problems at zero-speed which is an unobservable state point. The proposed observer based on higher order sliding mode (HOSM) is designed in order to ensure robustness against disturbances and to avoid the chattering phenomenon which is inherent in standard first order sliding modes. The stability and finite time convergence of the developed observer are studied and discussed. Experimental results are carried out to illustrate the effectiveness and robustness of the proposed observer. d dt P J L L i i f J T J [ sin( ) cos( ) ] 2 1 v v l J T J ω −

“…Obviously, the control laws with finite-time convergence are more desirable. Besides faster convergence rates, the closed-loop systems under finite-time control usually demonstrate higher accuracy, better disturbance rejection properties and robustness against uncertainties [18][19][20][21][22][23]. For the tracking control problem of nonholonomic mobile robot systems, some finitetime control laws have been proposed [24][25].…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Tracking Control for Nonholonomic Mobile Robots Based on Visual Servoing

Ou¹,

Li²,

Wang³

2013

This paper investigates the finite-time tracking problem of nonholonomic mobile robots in kinematic models via visual servoing in the presence of parametric uncertainties associated with the camera system. First of all, a camera-objective visual kinematic model is introduced by utilizing the pinhole camera model. Second, a unified tracking error system between the camera-objective visual servoing model and the desired reference trajectory is introduced. Third, based on the unified error dynamics and by using the finite-time control method, continuous finite-time controller laws are designed to solve the finite-time tracking problem for the mobile robot in the presence of parametric uncertainties associated with the camera system. Rigorous proof shows that the desired reference trajectory can be tracked in finite time. Finally, an example is employed to verify the efficiency of the proposed methods.