Robust stability and instability of nonlinear feedback system with uncertainty-dependent equilibrium

2014 ◽  
Author(s):  
Masaki Inoue ◽  
Takayuki Arai ◽  
Jun-ichi Imura ◽  
Kenji Kashima ◽  
Kazuyuki Aihara
Keyword(s):  
Robust Stability ◽  
Feedback System ◽  
Nonlinear Feedback ◽  
Stability And Instability

scholarly journals A Flexible Nonlinear Feedback System That Captures Diverse Patterns of Adaptation and Rebound

2008 ◽  
Vol 10 (1) ◽  
pp. 70-83 ◽  
Author(s):  
Johan Gabrielsson ◽  
Lambertus A. Peletier
Keyword(s):  
Feedback System ◽  
Nonlinear Feedback

scholarly journals Numerical Computation of Lower Bounds of Structured Singular Values

2018 ◽  
Vol 11 (3) ◽  
pp. 844-868
Author(s):  
M. Fazeel Anwar ◽  
Mutti-Ur Rehman
Keyword(s):  
System Theory ◽  
Linear Algebra ◽  
Lower Bounds ◽  
Robust Stability ◽  
Numerical Approximation ◽  
Singular Values ◽  
Numerical Linear Algebra ◽  
Linear Feedback ◽  
Feedback Systems ◽  
Stability And Instability

In this article we consider the numerical approximation of lower bounds of Structured Singular Values, SSV. The SSV is a wellknown mathematical quantity which is widely used to analyse and syntesize the robust stability and instability analysis of linear feedback systems in control theory. It links a bridge between numerical linear algebra and system theory. The computation of lower bounds of SSV by means of ordinary differential equations based technique is presented. The obtained numerical results for the lower bounds of SSV are compared with the well-known MATLAB function mussv available in MATLAB control toolbox.

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

2017 ◽  
Vol 24 (13) ◽  
pp. 2760-2781
Author(s):  
Xiao-Xiao Liu ◽  
Xing-Min Ren
Keyword(s):  
Nonlinear Control ◽  
Vibration Suppression ◽  
Estimation Method ◽  
Feedback System ◽  
Random Excitation ◽  
Point Estimation ◽  
Maximum Principles ◽  
Moving Mass ◽  
Nonlinear Feedback ◽  
Point Estimation Method

This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.

Stability of a Nonlinear Feedback System in the Presence of Gaussian Noise

1962 ◽  
Vol 84 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Rangasami Sridhar ◽  
Rufus Oldenburger
Keyword(s):  
Gaussian Noise ◽  
Natural Extension ◽  
Feedback System ◽  
Frequency Component ◽  
Analog Computer ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Describing Function ◽  
Power Spectral ◽  
Describing Function Method

A stability criterion for certain types of nonlinear feedback systems in the presence of Gaussian noise is established here. This criterion may be considered as a natural extension of the describing function method. It is assumed that the lowest frequency component in the power spectral density of the noise is at least ten times higher than the highest significant frequency of the system. The method developed here is applicable to feedback systems with just one instantaneous, nonmemory type nonlinearity in the loop. The results mentioned in this paper have been experimentally verified on an analog computer. The theory explained here may be used by the designer to predict the manner in which noise will affect the performance of a system.

Robust Stability of Nonlinear Feedback Systems With Parameter Deviations and Perturbed Nonlinearities

1997 ◽  
Vol 119 (1) ◽  
pp. 133-135
Author(s):  
Hayao Miyagi ◽  
Kimiko Kawahira ◽  
Norio Miyagi
Keyword(s):  
Robust Stability ◽  
Direct Method ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Individual Parameter ◽  
Nominal System ◽  
Additive Type ◽  
The Stability ◽  
Parameter Deviation ◽  
Nonlinear Feedback Systems

Robust stability of perturbed nonlinear feedback systems subjected to plant variations is investigated by using the direct method of Lyapunov. To establish the stability of the nominal system, the multivariable Popov criterion is utilized first. Then the stability of the system with parameter deviations and perturbed nonlinearities is studied. In this paper, an additive-type of parameter deviations are considered. The feature of the proposed method is that the tolerable range of individual parameter deviation and the conditions for the perturbed nonlinearities are simultaneously obtainable.

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