The probability density and level-crossings of first-order non-linear systems driven by the random telegraph signal†

1977 ◽  
Vol 25 (2) ◽  
pp. 283-292 ◽  
Author(s):  
R. F. PAWULA
Keyword(s):  
Probability Density ◽  
Linear Systems ◽  
Level Crossings ◽  
Random Telegraph Signal ◽  
First Order ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Linear Control Systems ◽  
First Order ◽  
Curved Manifolds ◽  
Non Linear ◽  
Covariant Derivation ◽  
Non Linear Systems ◽  
And Control

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

scholarly journals Oscillations in the first order non-linear systems with delay. I. Autonomous systems

1990 ◽  
Vol 12 (2) ◽  
pp. 1-5
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Tien Khiem
Keyword(s):  
Linear Systems ◽  
Asymptotic Method ◽  
Autonomous Systems ◽  
First Order ◽  
Non Linear ◽  
Non Linear Systems

Contrary to the systems without delay, in the first order systems with delay may be an undraped oscillation, which is constructed in this paper by means of the asymptotic method. The elf-excited oscillations in the Duffing and Van-De-Pol systems are considered.

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