{"product_id":"l2-gain-and-passivity-techniques-in-nonlinear-control-9783319842943","title":"L2-Gain and Passivity Techniques in Nonlinear Control","description":"\u003cp\u003e • Author(s): Arjan van der Schaft\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Artificial Intelligence - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis standard text gives a unified treatment of passivity and L\u003csub\u003e2\u003c\/sub\u003e-gain theory for nonlinear state space systems, preceded by a compact treatment of classical passivity and small-gain theorems for nonlinear input-output maps. The synthesis between passivity and L\u003csub\u003e2\u003c\/sub\u003e-gain theory is provided by the theory of dissipative systems. Specifically, the small-gain and passivity theorems and their implications for nonlinear stability and stabilization are discussed from this standpoint. The connection between L\u003csub\u003e2\u003c\/sub\u003e-gain and passivity via scattering is detailed.\u003c\/p\u003e \u003cp\u003eFeedback equivalence to a passive system and resulting stabilization strategies are discussed. The passivity concepts are enriched by a generalised Hamiltonian formalism, emphasising the close relations with physical modeling and control by interconnection, and leading to novel control methodologies going beyond passivity.\u003c\/p\u003e \u003cp\u003eThe potential of L\u003csub\u003e2\u003c\/sub\u003e-gain techniques in nonlinear control, including a theory of all-pass factorizations of nonlinear systems, and of parametrization of stabilizing controllers, is demonstrated. The nonlinear H-infinity optimal control problem is also treated and the book concludes with a geometric analysis of the solution sets of Hamilton-Jacobi inequalities and their relation with Riccati inequalities for the linearization.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e-\u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e L\u003csub\u003e2\u003c\/sub\u003e-Gain and Passivity Techniques in Nonlinear Control (third edition) is thoroughly updated, revised, reorganized and expanded. Among the changes, readers will find: \u003c\/p\u003e \u003cp\u003e\u003cb\u003e-\u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e updated and extended coverage of dissipative systems theory\u003c\/p\u003e \u003cp\u003e\u003cb\u003e-\u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e substantial new material regarding converse passivity theorems and incremental\/shifted passivity\u003c\/p\u003e - coverage of recent developments on networks of passive systems with examples\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e-\u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e a completely overhauled and succinct introduction to modeling and control of port-Hamiltonian systems, followed by an exposition of port-Hamiltonian formulation of physical network dynamics\u003c\/p\u003e \u003cb\u003e-\u003c\/b\u003e updated treatment of all-pass factorization of nonlinear systems\u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eThe book provides graduate students and researchers in systems and control with a compact presentation of a fundamental and rapidly developing area of nonlinear control theory, illustrated by a broad range of relevant examples stemming from different application areas.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45276984574103,"sku":"9783319842943","price":16714.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783319842943.webp?v=1769287174","url":"https:\/\/atlanticbooks.com\/products\/l2-gain-and-passivity-techniques-in-nonlinear-control-9783319842943","provider":"Atlantic Books","version":"1.0","type":"link"}