On the stability of limit cycles in nonlinear feedback systems: Analysis using describing functions

1982 ◽  
Author(s):  
R. Miller ◽  
A. Michel ◽  
Gary Krenz
Keyword(s):  
Limit Cycles ◽  
Systems Analysis ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Describing Functions ◽  
The Stability ◽  
Nonlinear Feedback Systems

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.

Bounded-Input-Bounded-Output Stability of Nonlinear Feedback Systems in a Volterra Representation

2000 ◽  
Author(s):  
John W. Glass ◽  
Matthew A. Franchek
Keyword(s):  
Stability Condition ◽  
Closed Loop ◽  
Controller Design ◽  
External Disturbance ◽  
Design Procedure ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Volterra Kernels ◽  
The Stability ◽  
Nonlinear Feedback Systems

Abstract Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is nonzero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity-norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L∞. These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class of nonlinear feedback systems.

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