On the stability of a class of nonlinear control systems

2015 ◽  
Vol 80 (3) ◽  
pp. 1245-1256 ◽  
Author(s):  
M. H. Noori Skandari
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Nonlinear Control Systems ◽  
The Stability

A New Approach to Popov Criterion for Stability Analysis of Nonlinear Control Systems

2012 ◽  
Vol 463-464 ◽  
pp. 1549-1552
Author(s):  
Ivan Svarc
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Control Systems ◽  
Transfer Functions ◽  
Sufficient Conditions ◽  
Nonlinear Control Systems ◽  
Engineering Practice ◽  
The Stability ◽  
The Given

The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The tables includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically. Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.

A New Algorithm for Limit Cycle Analysis of Nonlinear Control Systems

1988 ◽  
Vol 110 (3) ◽  
pp. 272-277 ◽  
Author(s):  
V. K. Pillai ◽  
H. D. Nelson
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Limit Cycle ◽  
Error Function ◽  
Numerical Procedure ◽  
Nonlinear Control Systems ◽  
Critical System ◽  
Describing Functions ◽  
The Stability ◽  
Generalized Newton

A numerical method is presented for the limit cycle analysis of multiloop nonlinear control systems with multiple nonlinearities. Describing functions are used to model the first harmonic gains of the nonlinearities. Existence of a limit cycle is sought by driving the least damped eigenvalues to the imaginary axis. The evolution of the limit cycle is studied next as a function of a critical system-parameter. It is shown that by defining a suitable error function it is possible to use both eigenvalue as well as the eigenvector sensitivities to formulate a generalized Newton-Raphson method to solve simultaneously for the updates of state variable amplitudes in a minimum norm sense. Several case studies have been presented and the development of a numerical procedure to test the stability of the limit cycle has also been reported.

Nonlinear Control Systems

2004 ◽  
Author(s):  
Christopher I. Byrnes ◽  
Alberto Isidori
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Nonlinear Control Systems

Normal forms for nonlinear control systems with scalar output

2005 ◽  
Vol 341 (9) ◽  
pp. 573-578
Author(s):  
Issa A. Tall ◽  
Moussa Balde
Keyword(s):  
Nonlinear Control ◽  
Control Systems ◽  
Normal Forms ◽  
Nonlinear Control Systems ◽  
Scalar Output
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