Numerical methods for the stability of time-periodic hybrid time-delay systems with applications

Abstract

• The pseudospectral tau method is extended to time-periodic hybrid time-delay systems. • The spectral element method is extended to time-periodic hybrid time-delay systems. • Stability analysis is performed for a haptic system involving both continuous and discrete delay terms. • Stability analysis is performed for a milling process with digitally controlled active vibration suppression. This paper extends two numerical methods for the stability analysis of a class of time-periodic hybrid time-delay systems. In particular, the pseudospectral tau and spectral element methods are extended to hybrid systems. The analyzed delay-differential equation involves delayed terms with both continuous and piecewise constant arguments, in other words, it involves delays both without and with zero-order hold, respectively. The analyzed class of hybrid systems can be used to describe time-periodic hereditary processes subjected to digital feedback control. The proposed numerical algorithms are applied to the mathematical models of haptic systems and milling processes subjected to digital feedback control.