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- W3214944131 abstract "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 <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$[mathcal {K},mathcal {KL}]$ </tex-math></inline-formula> sectors. Moreover, a mathematical relation is proposed between the sectors to define a discrete-time <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$[mathcal {K},mathcal {KL}]$ </tex-math></inline-formula> sector as a subset of the continuous-time <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$[mathcal {K},mathcal {KL}]$ </tex-math></inline-formula> 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." @default.
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- W3214944131 date "2022-04-01" @default.
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- W3214944131 title "Design of Nonlinear Sectors With Comparison Functions" @default.
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