Input-Output Stability Analysis with Magnetic Hysteresis Non-Linearity - A Class of Multipliers,

1984 ◽  
Author(s):  
M. G. Safonov ◽  
K. Karimlou
Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1246
Author(s):  
Constantin Voloşencu

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers.


1974 ◽  
Vol 96 (3) ◽  
pp. 315-321 ◽  
Author(s):  
G. Jumarie

Sampled-data, nonlinear, distributed systems, which exhibit a structure similar to that of the standard closed loop with lumped parameter, are investigated from the viewpoint of their input-output stability. These systems are governed by operational equations involving discrete Laplace-Green kernels. Their feedback gains are bounded by upper and lower values which depend explicitly on the time and the distributed parameter. The main result is: an input-output stability theorem is given which applies both in L∞ (O, ∞) and L2 (O, ∞). This criterion, which may be considered as being an extension of the ≪circle criterion≫, involves the mean square value on the bounds of the feedback gain. Stability conditions for continuous systems are derived from this result. In the special case of systems with distributed periodical time-varying feedback gains, a stability criterion is given which applies in Marcinkiewicz space M2 (O, ∞). This result which involves the mean square value of the feedback gain is generally less restrictive than the L2 (O, ∞) stability criterion mentioned above.


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