Geodesic
Stability and sliding modes for a class of nonlinear time delay systems
Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 155-164.

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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 $\varphi \colon \mathbb {R}\to \mathbb {R}$ 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.
DOI : 10.21136/MB.2011.141578
Classification : 34A36, 34D20, 34K20, 93C23, 93D10
Keywords: time lag; extended nonlinearity; absolute stability 
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Răsvan, Vladimir. Stability and sliding modes for a class of nonlinear time delay systems. Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 155-164. doi : 10.21136/MB.2011.141578. http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141578/

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