Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

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Theory of Dissipative Systems

The important concept of dissipativity developed by Willems [272, 273, 274], and later studied by Hill and Moylan [131]-[134], [202] has proven very successful in many feedback design synthesis problems [30]-[32], [233, 264, 272, 273]. This concept which was originally inspired from electrical network considerations, in particular passive circuits [30, 31, 32], generalizes many other important concepts of physical systems such as positive-realness [233], passivity [77] and losslessness [74]. As such, many important mathematical relations of dynamical systems such as the bounded-real lemma, positive-real lemma, the existence of spectral-factorization and finite ${\mathcal{L}}_p$-gain of linear and nonlinear systems have been ...