By Arjan van der Schaft
This normal textual content supplies a unified remedy of passivity and L2-gain thought for nonlinear kingdom area platforms, preceded by means of a compact therapy of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis among passivity and L2-gain concept is supplied by way of the idea of dissipative structures. in particular, the small-gain and passivity theorems and their implications for nonlinear balance and stabilization are mentioned from this viewpoint. the relationship among L2-gain and passivity through scattering is detailed.
Feedback equivalence to a passive method and ensuing stabilization ideas are mentioned. The passivity ideas are enriched by means of a generalised Hamiltonian formalism, emphasising the shut relatives with actual modeling and keep watch over through interconnection, and resulting in novel keep watch over methodologies going past passivity.
The strength of L2-gain recommendations in nonlinear regulate, together with a conception of all-pass factorizations of nonlinear structures, and of parametrization of stabilizing controllers, is confirmed. The nonlinear H-infinity optimum keep watch over challenge can also be handled and the e-book concludes with a geometrical research of the answer units of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization.
· L2-Gain and Passivity strategies in Nonlinear keep watch over (third variation) is carefully up to date, revised, reorganized and improved. one of the alterations, readers will find:
· up to date and prolonged insurance of dissipative structures theory
· massive new fabric concerning communicate passivity theorems and incremental/shifted passivity · insurance of modern advancements on networks of passive structures with examples
· a very overhauled and succinct advent to modeling and regulate of port-Hamiltonian structures, by way of an exposition of port-Hamiltonian formula of actual community dynamics
· up-to-date therapy of all-pass factorization of nonlinear systems
The publication offers graduate scholars and researchers in platforms and keep an eye on with a compact presentation of a basic and quickly constructing quarter of nonlinear keep watch over conception, illustrated through a huge diversity of suitable examples stemming from various software areas.