Stability and maximum boundedness of processes in systems with pulse- width modulation
type: Item
instance of: scholarly article
title: Stability and maximum boundedness of processes in systems with pulse- width modulation
zbMATH Open document ID: 0663.93059
author: O. Ya. Karetnyj
author: M. L. Yudkevich
author: Arkadiĭ Khaimovich Gelig
published in: Automation and Remote Control
publication date: 1988-01-01T00:00:00Z
review text: Consider the integral equation \[ \sigma(t)= \alpha_ 0+\alpha(t)+\psi(t)-\int^{t}_{0} [\rho+\gamma(t-\tau)] \phi(\tau)d\tau \] where \(\phi(t)=sgn \sigma(nT)\) \(nT\leq t\leq nT+\tau_ n\), \(\phi(t)=0\), \(nT+\tau_ n<t\leq (n+1)T\) and \(\tau_ n\) is defined by some nonlinear equation. Here \(\gamma (\cdot)\in L^ 1(0,\infty),\) \(| {\dot \gamma}(t)| +{\ddot \gamma}(t)| \leq c_ 0e^{- \alpha t}\) and \(\psi(\cdot)\) is a piecewise continuous function. Frequency domain conditions expressed in terms of \({\tilde \gamma}(\sigma)\), the Laplace transform of \(\gamma(t)\), are obtained for the asymptotic behaviour of the difference of two arbitrary solutions of the integral equation as well as for dissipativity (ultimate boundedness) of the solutions.
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 93D10
zbMATH DE Number: 4085546
zbMATH Keywords: integral equation
zbMATH Keywords: Frequency domain conditions
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: ultimate boundedness
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4085546