scholarly journals Global Stability and Exponential Decay of Processes in Nonlinear Feedback Systems with Different Fractional Orders

J ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 328-340
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Global Stability ◽  
Exponential Decay ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Gain Matrix ◽  
Fractional Orders ◽  
Nonlinear Feedback Systems

The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this class of positive nonlinear systems are established. Sufficient conditions for the exponential decay of processes in fractional nonlinear systems are given. Procedures for computation of a gain matrix characterizing the class of nonlinear elements are proposed and illustrated by examples.

Global stability of fractional different orders nonlinear feedback systems with positive linear parts and interval state matrices

2021 ◽  
Vol 24 (3) ◽  
pp. 950-962
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Global Stability ◽  
Positive Feedback ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Stability Conditions ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Fractional Orders ◽  
Nonlinear Feedback Systems

Abstract The global stability of continuous-time fractional orders nonlinear feedback systems with positive linear parts and interval state matrices is investigated. New sufficient conditions for the global stability of this class of positive feedback nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple example.

scholarly journals Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 17-20
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Positive Time

The global stability of positive  discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.

THE PERFORMANCE OF DIFFERENT DITHER SIGNALS IN NONLINEAR SYSTEMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 2507-2520 ◽  
Author(s):  
SENG-CHI CHEN ◽  
HSUN-HENG TSAI
Keyword(s):  
Nonlinear Systems ◽  
High Frequency ◽  
Nonlinear Element ◽  
Wave Form ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
High Frequency Signal ◽  
Wave Forms ◽  
Set Up ◽  
Nonlinear Feedback Systems

Dither is a high frequency signal which is introduced into a nonlinear system with the object of augmenting stability, quenching undesirable limit cycle, and altering the apparent nonlinear element characteristics. In this paper, we investigate the performance of various high frequency dither signals with different wave forms in nonlinear feedback systems. Meanwhile, an analog experimental device is set up to simulate the nonlinear systems, which consists of dither and a nonlinear element such as a relay or a limiter. A describing function and an equivalent nonlinearity method are used to evaluate the dither performance. The performance of various dither signals having a certain wave form is examined through these studies, and the results could evaluate effectiveness of these dither-injection techniques into nonlinear feedback systems.

Stability of Subharmonic Oscillations in Nonlinear Systems

1964 ◽  
Vol 86 (1) ◽  
pp. 116-120 ◽  
Author(s):  
Rufus Oldenburger ◽  
Robert E. Nicholls
Keyword(s):  
Nonlinear Systems ◽  
Necessary Conditions ◽  
Analog Computer ◽  
Higher Order ◽  
Nonlinear Element ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Describing Function ◽  
Subharmonic Oscillation ◽  
Nonlinear Feedback Systems

This paper presents a method for finding necessary conditions such that a subharmonic oscillation may exist in certain types of nonlinear feedback systems. The method is applicable to feedback systems with one, instantaneous, nonmemory-type, nonlinear element. Equations are derived giving the fundamental output of a nonlinear element when forced by two sine waves of integer ratio frequency. Normal describing-function assumptions are made with regard to attenuation of higher-order harmonics. An example of a system incorporating a perfect relay is presented. The results of the analysis have been verified experimentally on the analog computer.

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