Lyapunov stability analysis and controller design for rational polynomial systems using sum of squares programming

2017 ◽  
Author(s):  
Mohsen Vatani ◽  
Morten Hovd
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Controller Design ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Rational Polynomial ◽  
Lyapunov Stability Analysis

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Polynomial control design for polynomial systems: A non-iterative sum of squares approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1993-2004
Author(s):  
Mohsen Rakhshan ◽  
Navid Vafamand ◽  
Mohammad Mehdi Mardani ◽  
Mohammad-Hassan Khooban ◽  
Tomislav Dragičević
Keyword(s):  
Controller Design ◽  
Time Derivative ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Continuous Stirred Tank Reactor ◽  
Wide Range ◽  
Convex Problem ◽  
Lyapunov Matrix ◽  
Different Chaotic Systems ◽  
Real Time Simulations

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.

LYAPUNOV STABILITY ANALYSIS OF DISCRETE-TIME ROBUST ADAPTIVE SUPER-TWISTING SLIDING MODE CONTROLLER

2021 ◽  
pp. 1-0
Author(s):  
Guilherme Vieira Hollweg ◽  
Paulo Jefferson Dias de Oliveira Evald ◽  
Deise Maria Cirolini Milbradt ◽  
Rodrigo Varella Tambara ◽  
Hilton Abilio Grundling
Keyword(s):  
Stability Analysis ◽  
Lyapunov Stability ◽  
Discrete Time ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Lyapunov Stability Analysis ◽  
Robust Adaptive

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.

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