Abstract: In this note we consider stability analysis of discrete-time discontinuous systems using Lyapunov functions. We demonstrate via simple examples that the classical second method of Lyapunov ...

The Julia library SummationByPartsOperators.jl provides a unified interface of different discretization approaches including finite difference, Fourier pseudospectral, continuous Galerkin, and ...

Exasim is an open-source software for generating high-order discontinuous Galerkin (DG) codes to numerically solve parametrized partial differential equations (PDEs) on different computing platforms ...

Abstract: The discontinuous dynamical behavior of a modified Duffing-Rayleigh system with a piecewise quadratic function is studied. The necessary and sufficient conditions for motion switchability at ...

Numerically solving seismic wave equations is vital to large-scale forward modeling and full waveform inversion. In this paper, a new modified symplectic discontinuous Galerkin (MSDG) method is ...

Inspired by the survival war between the “spear” of mantis shrimps with Bouligand-type microstructures and the “shield” of abalone with nacreous staggered architectures, we design an architecture, a ...

In this study, the stability for a class of sampled-data Takagi-Sugeno (T-S) fuzzy systems with state quantization was investigated. Using the discontinuous Lyapunov-Krasoskii functional (LKF) ...

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