PID Passivity-Based Control of Nonlinear Systems with Applications. Romeo Ortega
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upper K Subscript upper P Baseline y 0 minus upper K Subscript upper I Baseline left-bracket gamma left-parenthesis x right-parenthesis minus gamma left-parenthesis x Superscript star Baseline right-parenthesis right-bracket comma"/>
which exactly coincides with the control generated with the PI‐PBC evaluated at
The details of this construction are given in Chapter 6, where we also prove that the set of solutions of the partial differential equations (PDEs) that must be solved to generate the invariant foliation
Bibliography
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Notes
1 1 Essentially, it is necessary to ensure that the control law 2.1 can be computed without differentiation nor singularities. We will elaborate on this issue in Section 2.2.
2 2 We recall that a necessary condition for passivity of the system is that the relative degree is smaller or equal to one (van der Schaft, 2016).
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