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Extending hysteresis operators to spaces of piecewise continuous functions. (English) Zbl 1042.47049
Motivated by problems of sampled-data control in systems with input hysteresis, the authors develop a theory of scalar hysteresis operators acting on piecewise continuous functions with possible isolated jumps. Hysteresis operators are understood in their maximal generality, that is, as causal rate-independent mappings in appropriate spaces of functions of time.

47J40 Equations with nonlinear hysteresis operators
93B52 Feedback control
34C55 Hysteresis for ordinary differential equations
Full Text: DOI
[1] Araki, M., Recent developments in digital control theory, (), 251-260
[2] Banks, H.T.; Smith, R.C.; Wang, Y., Smart material structures: modeling, estimation and control, (1996), Masson Paris · Zbl 0882.93001
[3] Brokate, M., Hysteresis operators, (), 1-38 · Zbl 0836.35065
[4] Brokate, M.; Sprekels, J., Hysteresis and phase transitions, (1996), Springer-Verlag New York · Zbl 0951.74002
[5] Krasnosel’skiı̆, M.A.; Pokrovskiı̆, A.V., Systems with hysteresis, (1989), Springer-Verlag Berlin
[6] Logemann, H.; Mawby, A.D., Low-gain integral control of infinite-dimensional regular linear systems subject to input hysteresis, (), 255-293
[7] Logemann, H.; Mawby, A.D., Discrete-time and sampled-data low-gain control of infinite-dimensional linear systems in the presence of input hysteresis, SIAM J. control optim., 41, 113-140, (2002) · Zbl 1036.47048
[8] Macki, J.W.; Nistri, P.; Zecca, P., Mathematical models for hysteresis, SIAM rev., 35, 94-123, (1993) · Zbl 0771.34018
[9] Visintin, A., Differential models of hysteresis, (1994), Springer-Verlag Berlin · Zbl 0820.35004
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