A chain observer for a class of nonlinear systems with long multiple delays in output measurements

2018 ◽  
Author(s):  
Boubekeur Targui ◽  
O. Hernandez-Gonzalez ◽  
C.M. Astorga-Zaragoza ◽  
M. Pouliquen ◽  
O. Gehan
Keyword(s):  
Nonlinear Systems ◽  
Multiple Delays ◽  
A Chain

A Chain Observer for Nonlinear Systems with Multiple Time-Varying Measurement Delays

2014 ◽  
Vol 52 (3) ◽  
pp. 1862-1885 ◽  
Author(s):  
Filippo Cacace ◽  
Alfredo Germani ◽  
Costanzo Manes
Keyword(s):  
Nonlinear Systems ◽  
Multiple Time ◽  
Time Varying ◽  
A Chain

scholarly journals New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2872
Author(s):  
Sergey Kashchenko ◽  
Anna Tolbey
Keyword(s):  
Differential Operator ◽  
Nonlinear Systems ◽  
Original Problem ◽  
Spatial Variable ◽  
Local Behavior ◽  
Spatial Variables ◽  
Irregular Solution ◽  
Spatially Distributed ◽  
A Chain ◽  
Special Differential Operator

For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of the Schrödinger type—quasinormal forms—whose nonlocal dynamics determines the local behavior of solutions to the original problem, as t→∞. On their basis, results are obtained on the asymptotics in the main solution of the FPU equation and on the interaction of waves moving in opposite directions. The problem of “perturbing” the number of N elements of a chain is considered. In this case, instead of the differential operator, with respect to one spatial variable, a special differential operator, with respect to two spatial variables appears. This leads to a complication of the structure of an irregular solution.

scholarly journals On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Switched Systems ◽  
Multiple Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Arbitrary Switching ◽  
Aggregation Techniques ◽  
Robust Stability Analysis

This paper provides new sufficient conditions on robust asymptotic stability for a class of uncertain discrete-time switched nonlinear systems with time varying delays. The main focus will be dedicated to development of new algebraic criteria to break with classical criteria in terms of linear matrix inequalities (LMIs). Firstly, by contracting a new common Lyapunov-Krasovskii functional as well as resorting to the M-matrix proprieties, a novel robust stability criterion under arbitrary switching signals is derived. Secondly, the obtained result is extended for a class of switched nonlinear systems modeled by a set of differences equations by applying the aggregation techniques, the norm vector notion, and the Borne-Gentina criterion. Furthermore, a generalization for switched nonlinear systems with multiple delays is proposed. The main contribution of this work is that the obtained stability conditions are algebraic and simple. In addition, they provide a solution of the most difficult problem in switched systems, which is stability under arbitrary switching, and enable avoiding searching a common Lyapunov function considered as a very difficult task even for some low-order linear switched systems. Finally, two examples are given, with numerical simulations, to show the merit and effectiveness of the proposed approach.

Robust asymptotic tracking control of a chain of integrator nonlinear systems with input constraint and hysteresis nonlinearity

2016 ◽  
Vol 38 (12) ◽  
pp. 1500-1508 ◽  
Author(s):  
Zhenle Dong ◽  
Jianyong Yao ◽  
Dawei Ma
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Controller Design ◽  
Input Constraint ◽  
Hysteresis Nonlinearity ◽  
Asymptotic Tracking ◽  
Disturbance Term ◽  
A Chain ◽  
Constant Slope ◽  
Bounded Disturbance

This paper focuses on the problem of tracking control of a chain of integrator nonlinear systems with input constraint and hysteresis nonlinearity. Input constraint, always existing in physical systems, has been proved a source of performance degradation. To handle this issue, an effective hyperbolic saturation function is employed, which is bounded no matter how the disturbances and error signals change. Furthermore, hysteresis nonlinearity, which may also limit the system performance, is modelled as a combination of a linear term with constant slope and a bounded disturbance term, which makes it possible to be integrated in the model based controller design. The robust integral of the sign of error (RISE) control is synthesized to guarantee the asymptotic tracking performance in the presence of parametric uncertainties and unmodelled nonlinearities such as external disturbances and unmodelled hysteresis nonlinearity. The closed-loop stability is proved via Lyapunov analysis. Some simulations are carried out to verify the effectiveness of the proposed controller.

Stabilizing a Chain of Integrators Using Multiple Delays

2004 ◽  
Vol 49 (5) ◽  
pp. 802-807 ◽  
Author(s):  
S.-I. Niculescu ◽  
W. Michiels
Keyword(s):  
Multiple Delays ◽  
A Chain
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