Stability Analysis for Switched Uncertain Nonlinear Systems With Dwell Time and Delay in the Active Mode Detection

2019 ◽  
Vol 3 (2) ◽  
pp. 362-367 ◽  
Author(s):  
L. Etienne ◽  
K. M. D. Motchon ◽  
S. Lecoeuche
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Dwell Time ◽  
Uncertain Nonlinear Systems ◽  
Active Mode ◽  
Mode Detection

scholarly journals Sliding mode learning control of uncertain nonlinear systems with Lyapunov stability analysis

2018 ◽  
Vol 41 (6) ◽  
pp. 1750-1760
Author(s):  
Erkan Kayacan
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Stability ◽  
Sliding Mode ◽  
Learning Control ◽  
System Stability ◽  
Uncertain Nonlinear Systems ◽  
System Behaviour ◽  
Lyapunov Stability Analysis ◽  
The Stability

This paper addresses the Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a type-2 neuro-fuzzy controller (T2NFC) learns system behaviour so that the T2NFC completely takes over overall control of the system in a very short time period. The stability of the sliding mode learning algorithm has been proven in the literature; however, it is restrictive for systems without overall system stability. To address this shortcoming, a novel control structure with a novel sliding surface is proposed in this paper, and the stability of the overall system is proven for nth-order uncertain nonlinear systems. To investigate the capability and effectiveness of the proposed learning and control algorithms, the simulation studies have been carried out under noisy conditions. The simulation results confirm that the developed SMLC algorithm can learn the system behaviour in the absence of any mathematical model knowledge and exhibit robust control performance against external disturbances.

Delay-Dependent Robust Stability Analysis for Uncertain Nonlinear Systems

2012 ◽  
Vol 591-593 ◽  
pp. 577-579
Author(s):  
Jing Song ◽  
Kun Qiu
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Riccati Equation ◽  
Robust Stability ◽  
Algebraic Riccati Equation ◽  
Delay Systems ◽  
Uncertain Nonlinear Systems ◽  
Robust Stability Analysis ◽  
High Level

As a popular topic, robust stability for uncertain systems with time delay have been widely studied in various engineering, biological, economical, electronic and dynamical systems, nerve network and so on. Recently, many researchers have paid a lot of attentions on the problem of robust stability for uncertain nonlinear systems with time delay. In this paper, a type of uncertain nonlinear delay systems has been considered in robust stability analysis. A novel robust stability criterion of the system is derived by using Lyapunov method and quadratic stability theory. A new upper bound with high-level infinite small on time delay based on Hariwity matrix and a solvable algebraic Riccati equation is presented. The main results are as follows: Through Lyapunov function and a solvable algebraic Riccati equation, we obtain the criterion of robust stability (exponential stability) for uncertain nonlinear systems with time delay.

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