Design of Nonlinear Sectors With Comparison Functions

In this brief, a class of comparison functions is defined to design the nonlinear sectors for continuous/discrete-time analysis and ensure uniformity in the solution. The results of Matrosov's proof are incorporated to fragment the state-space to design both the continuous and the discrete-time...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2022-04, Vol.69 (4), p.2251-2255
Main Authors: Sachan, Ankit, Deveerasetty, Kranthi Kumar, Soni, Sandeep Kumar
Format: Article
Language:English
Subjects:
Asymptotic stability
Circuits and systems
continuous-time [K
discrete-time [K
KL] sector
Liapunov functions
Mathematical analysis
Matrosov theorem
region of attraction
Series expansion
Stability analysis
Taylor series
Taylor’s series expansion
Thermal stability
Three-dimensional displays
Trajectory
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Summary:In this brief, a class of comparison functions is defined to design the nonlinear sectors for continuous/discrete-time analysis and ensure uniformity in the solution. The results of Matrosov's proof are incorporated to fragment the state-space to design both the continuous and the discrete-time [\mathcal {K},\mathcal {KL}] sectors. Moreover, a mathematical relation is proposed between the sectors to define a discrete-time [\mathcal {K},\mathcal {KL}] sector as a subset of the continuous-time [\mathcal {K},\mathcal {KL}] sector. Taylor's series expansion relates the difference of the candidate-Lyapunov function to the derivative of the candidate-Lyapunov function for sampled-data, as well as higher-order derivatives. The validation of the result is verified by using the Van der Pol equation.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2021.3130636