Differential and Integral Equations
- Differential Integral Equations
- Volume 15, Number 2 (2002), 167-189.
Sliding modes in Banach spaces
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.
Differential Integral Equations, Volume 15, Number 2 (2002), 167-189.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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