Abstract
In this chapter the general theory of dissipative systems is treated, laying much of the foundation for subsequent chapters.
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Notes
- 1.
Here it is additionally assumed that for allowed input functions \(u(\cdot )\) and generated output functions \(y(\cdot )\) the integral \(\int ^{t_1}_{t_0} s(u(t),y(t)) dt\) is well defined.
- 2.
Here we naturally restrict to continuous solutions.
- 3.
Here it is assumed that \(\dot{x} = f(x,u(x))\) has unique solutions on \([0,\infty )\) for all initial conditions.
- 4.
Note however that there does not always exist such a state of minimal internal energy. In particular \(\inf _x S_a(x)=0\) but not necessarily the minimum is attained.
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van der Schaft, A. (2017). Dissipative Systems Theory. In: L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-49992-5_3
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DOI: https://doi.org/10.1007/978-3-319-49992-5_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-49992-5
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