Vl. Răsvan, University of Craiova, Department of Automatic Control, A. I. Cuza str. 13, RO-200 585 Craiova, Romania, e-mail: vrasvan@automation.ucv.ro
Abstract: The following time delay system
\dot{x} = Ax(t) + \sum_1^rbq_i^*x(t-\tau_i)-b\varphi(c^*x(t))
is considered, where $\varphi \mathbb{R}\to\mathbb{R}$ may have discontinuities, in particular at the origin. The solution is defined using the "redefined nonlinearity" concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.
Keywords: time lag, extended nonlinearity, absolute stability
Classification (MSC 2010): 34A36, 34D20, 34K20, 93C23, 93D10
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