Differential and Integral Equations

Sliding modes in Banach spaces

Laura Levaggi

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Using differential inclusions and viability theory we define sliding modes for (feedback) controlled semilinear differential equations in Banach spaces. We compare this definition with the equivalent control method for infinite-dimensional systems proposed by V. Utkin and Yu. Orlov. We show that if the sliding manifold satisfies suitable regularity hypotheses and the semigroup is compact, the projected evolution found by means of the equivalent control and our sliding mode do coincide.

Article information

Differential Integral Equations, Volume 15, Number 2 (2002), 167-189.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93B12: Variable structure systems
Secondary: 34G25: Evolution inclusions 34H05: Control problems [See also 49J15, 49K15, 93C15] 49J24


Levaggi, Laura. Sliding modes in Banach spaces. Differential Integral Equations 15 (2002), no. 2, 167--189. https://projecteuclid.org/euclid.die/1356060871

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