Behavior of solutions of nonlinear systems of difference equations in a neighborhood of an invariant toroidal manifold

1989 ◽  
Vol 41 (1) ◽  
pp. 49-56
Author(s):  
Yu. A. Mitropol'skii ◽  
D. I. Martynyuk ◽  
V. Ya. Danilov
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Toroidal Manifold ◽  
Invariant Toroidal Manifold

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals On the solutions of some nonlinear systems of difference equations

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Elsayed M Elsayed ◽  
Hamdy El-Metwally
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations

scholarly journals Perturbations of Nonlinear Systems of Difference Equations

1996 ◽  
Vol 204 (2) ◽  
pp. 545-553 ◽  
Author(s):  
Rigoberto Medina
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations

Stabilizability for nonlinear systems of difference equations

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
Rigoberto Medina
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations

On a Solvable for Some Nonlinear Systems of Difference Equations

2015 ◽  
Vol 12 (10) ◽  
pp. 3432-3442
Author(s):  
M. M. El-Dessoky
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations

scholarly journals Periodic Solutions for a System of Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Shugui Kang ◽  
Bao Shi
Keyword(s):  
Nonlinear Systems ◽  
Critical Point ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Second Order ◽  
System Of Difference Equations

This paper deals with the second-order nonlinear systems of difference equations, we obtain the existence theorems of periodic solutions. The theorems are proved by using critical point theory.

A Theory of Index for Point Mapping Dynamical Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 185-190 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Difference Equations ◽  
Vector Fields ◽  
Time Difference ◽  
Point Mapping ◽  
Strongly Nonlinear

Dynamical systems governed by discrete time-difference equations are referred to as point mapping dynamical systems in this paper. Based upon the Poincare´ theory of index for vector fields, a theory of index is established for point mapping dynamical systems. Besides its intrinsic theoretic value, the theory can be used to help search and locate periodic solutions of strongly nonlinear systems.

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