Observer Design for Nonlinear Systems: An Approach Based on the Differential Mean Value Theorem.

2006 ◽  
Author(s):  
A. Zemouche ◽  
M. Boutayeb ◽  
G.I. Bara
Keyword(s):  
Nonlinear Systems ◽  
Mean Value ◽  
Observer Design ◽  
Mean Value Theorem ◽  
Differential Mean Value Theorem

Observer design for induction motor: an approach based on the mean value theorem

2014 ◽  
Vol 8 (4) ◽  
pp. 426-433 ◽  
Author(s):  
Mohamed Yacine Hammoudi ◽  
Abdelkarim Allag ◽  
Mohamed Becherif ◽  
Mohamed Benbouzid ◽  
Hamza Alloui
Keyword(s):  
Induction Motor ◽  
Mean Value ◽  
Observer Design ◽  
Mean Value Theorem ◽  
The Mean

scholarly journals Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Chunfang Miao ◽  
Yunquan Ke
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
First Order ◽  
Inequality Technique ◽  
Variable Substitution ◽  
Differential Mean Value Theorem

The existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks are investigated. First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

scholarly journals Real Time Stabilization of Lipschitz Nonlinear Systems with Nonlinear Output

2020 ◽  
Vol 53 (4) ◽  
pp. 493-498
Author(s):  
Assem Thabet ◽  
Ghazi Bel Haj Frej ◽  
Noussaiba Gasmi ◽  
Brahim Metoui
Keyword(s):  
Nonlinear Systems ◽  
Real Time ◽  
Nonlinear Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lipschitz Nonlinear Systems ◽  
Parameter Varying

This brief discusses a simple stabilization strategy for a class of Lipschitz nonlinear systems based on the transformation of nonlinear function to Linear Parameter Varying system. Due to the introduction of the Differential Mean Value Theorem (DMVT), the dynamic and output nonlinear functions are transformed into Linear Parameter Varying (LPV) functions. This allows to increase the number of decision variables in the constraint to be resolved and, then, get less conservative and more general Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of LMI with the introduction of a cost control to ensure closed-loop stability. Finally, Real Time Implementation (RTI) using a DSP device (ARDUINO UNO R3) to a typical robot is given to illustrate the performances of the proposed method with a comparison to some existing results.

scholarly journals Stabilization and Synchronization of Hyper-Chaotic Financial System Involved in Positive Interest Rate

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Financial System ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Pulse Control ◽  
Delayed Effect ◽  
Control Effect ◽  
Lyapunov Function Method ◽  
Mathematical Difficulties ◽  
Market Feedback ◽  
Differential Mean Value Theorem

In real financial market, the delayed market feedback and the delayed effect of government macro-control are inevitable. And both the delay of market feedback and the delay of macro-control effect bring about the mathematical difficulties in studying stabilization and synchronization of the hyper-chaotic financial system. However, employing Lyapunov function method, differential mean value theorem, suitable bounded hypotheses and pulse control technology results in the globally asymptotical stabilization and synchronization criteria. It is the first paper to drive the stabilization and synchronization criteria under the assumptions of the double delays. Finally, numerical examples illuminate the effectiveness of the proposed methods.

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