Some Sufficient Conditions for the Controllability of Linear and Nonlinear Systems

2014 ◽  
Author(s):  
Yuanhui Liu ◽  
Tianfu Xu
Keyword(s):  
Nonlinear Systems ◽  
Sufficient Conditions ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

scholarly journals Hyers-Ulam-Rassias Instability for Linear and Nonlinear Systems of Differential Equations

2019 ◽  
pp. 1-16
Author(s):  
Maher Nazmi Qarawani
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Systems Of Differential Equations ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

This paper considers Hyers-Ulam-Rassias instability for linear and nonlinear systems of differential equations. Integral sufficient conditions of Hyers-Ulam-Rassias instability and Hyers-Ulam instability for linear and nonlinear systems of differential equations are established. Illustrative examples will be given.

Positivity and Stability of Standard and Fractional Descriptor Continuous-Time Linear and Nonlinear Systems

2018 ◽  
Vol 19 (3-4) ◽  
pp. 299-307 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Linear And Nonlinear Systems ◽  
Time Linear

AbstractThe positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems are addressed. Necessary and sufficient conditions for the positivity of descriptor linear and sufficient conditions for nonlinear systems are established. Using an extension of Lyapunov method sufficient conditions for the stability of positive nonlinear systems are given. The considerations are extended to fractional nonlinear systems.

scholarly journals Preservation of Stability and Synchronization of a Class of Fractional-Order Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Armando Fabián Lugo-Peñaloza ◽  
José Job Flores-Godoy ◽  
Guillermo Fernández-Anaya
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Linear Part ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Fractional Order Systems ◽  
Nonlinear Part ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

We present sufficient conditions for the preservation of stability of fractional-order systems, and then we use this result to preserve the synchronization, in a master-slave scheme, of fractional-order systems. The systems treated herein are autonomous fractional differential linear and nonlinear systems with commensurate orders lying between 0 and 2, where the nonlinear ones can be described as a linear part plus a nonlinear part. These results are based on stability properties for equilibria of fractional-order autonomous systems and some similar properties for the preservation of stability in integer order systems. Some simulation examples are presented only to show the effectiveness of the analytic result.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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