A counter example to a recent result on the stability of non-linear systems

2009 ◽  
Vol 26 (3) ◽  
pp. 319-323 ◽  
Author(s):  
S. Muhammad ◽  
J. van der Woude
Keyword(s):  
Recent Result ◽  
Linear Systems ◽  
Counter Example ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability

Non-linear disturbance observer-based adaptive composite anti-disturbance control for non-linear systems with dynamic non-harmonic multisource disturbances

2017 ◽  
Vol 40 (12) ◽  
pp. 3458-3465 ◽  
Author(s):  
Zheng Wang ◽  
Jianping Yuan
Keyword(s):  
Linear Systems ◽  
Disturbance Observer ◽  
Control Structure ◽  
Non Linear ◽  
Linear Damping ◽  
Non Linear Systems ◽  
Complex Features ◽  
The Stability ◽  
Linear Disturbance ◽  
Adaptive Composite

In this paper, an adaptive composite anti-disturbance control structure is constructed for a class of non-linear systems with dynamic non-harmonic multisource disturbances. The key point of this paper is that a kind of non-harmonic disturbance, which has non-linear internal dynamics and complex features, is involved. A non-linear exogenous system is employed to describe the dynamic non-harmonic disturbances and several useful assumptions are introduced. By introducing a non-linear damping term, a novel adaptive non-linear disturbance observer is constructed. Based on the disturbance/uncertainty estimation and attenuation (DUEA) schemes, a composite anti-disturbance control structure is synthesized. Meanwhile, a new sufficient condition is derived and the stability of the closed-loop system is proved. Several illustrative examples are employed to demonstrate the effectiveness of the proposed method.

Inversion control of non-linear systems with an inverse NARX model identified using genetic algorithms

2000 ◽  
Vol 214 (4) ◽  
pp. 259-271 ◽  
Author(s):  
G-C Luh ◽  
C-Y Wu
Keyword(s):  
Genetic Algorithms ◽  
Linear Systems ◽  
Inverse Dynamics ◽  
Feedback Controller ◽  
Input Estimation ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Identification Model ◽  
Narx Model

The inverse dynamics approach has been widely utilized in the control problem of various practical non-linear systems in recent years. This paper demonstrates a feedforward-feedback controller scheme of a non-linear plant whose dynamics are unknown and uncertain. The feedforward controller, an inverse NARX model (non-linear autoregressive model with exogenous inputs), provides only coarse control, whereas the feedback controller is used to handle unmodelled dynamics and disturbance. The inverse NARX model is derived by inverting the forward NARX model identified using genetic algorithms. A parallel-type NARX model whose outputs of the identification model are fed back into the identification model is adopted in the identification procedure to include the stability examination numerically. Both experimental and simulation results demonstrate that the proposed controller provides very good performance in the problems of input estimation and output tracking.

On the stability of a class of general non-linear systems

2001 ◽  
Vol 291 (1) ◽  
pp. 11-16 ◽  
Author(s):  
I.M. Gléria ◽  
A. Figueiredo ◽  
T.M. Rocha Filho
Keyword(s):  
Linear Systems ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability

Coexistent of Solutions in Non-Linear Systems with Impacts

2014 ◽  
Vol 543-547 ◽  
pp. 1840-1843
Author(s):  
Jin Qian Feng ◽  
Yue Tang Rong ◽  
Jun Li Liu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Shooting Method ◽  
Duffing System ◽  
Coexistence Of Attractors ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Non Linear System

This paper proposes a corrected shooting method for a general non-linear system with impacts. We define the global Poincaré mapping for period orbits by the discontinuous mapping. It is suitable to construct the strategy of shooting method. As an illustrated example, we investigate the stability of period orbits in a Duffing system with impacts. In Addition, coexistence of attractors and bifurcations for period orbits are considered.

scholarly journals Stability of non-linear systems with time-varying delays

1980 ◽  
Vol 21 (4) ◽  
pp. 452-463
Author(s):  
R. M. Lewis
Keyword(s):  
Linear Systems ◽  
Time Delays ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability

AbstractA condition guranteeing the stability of linear systems with time delays in the interactions among elements is generalized to cover non-linear systems and discontinuous, unbounded delays.

The practical use of variation principles in the determination of the stability of non linear systems

1961 ◽  
Vol 2 (2) ◽  
pp. 153-188 ◽  
Author(s):  
J. N. Lyness ◽  
J. M. Blatt
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
Mathieu Equation ◽  
Iteration Procedure ◽  
Variation Principle ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Special Case

AbstractWe are interested in the motion of non linear systems. In this paper we use a variation principle and an iteration procedure in order to treat the stability of free oscillations against small disturbances of the initial conditions. It is found that approximations to the low lying stability lines can be obtained using the Rayleigh-Ritz variation principle and that these approximations can be consistently improved using an iteration procedure. These approximations are compared with the tabulated values in the special case of the Mathieu Equation. The results are in general a considerable improvement on those obtained using the usual Perturbation Theory, and have a much wider range of validity.

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