By R. Sepulchre

ISBN-10: 1447112458

ISBN-13: 9781447112457

Positive Nonlinear keep an eye on provides a large repertoire of positive nonlinear designs now not to be had in different works through widening the category of structures and layout instruments. numerous streams of nonlinear keep watch over idea are merged and directed in the direction of a positive answer of the suggestions stabilization challenge. research, geometric and asymptotic innovations are assembled as layout instruments for a large choice of nonlinear phenomena and buildings. Geometry serves as a advisor for the development of layout tactics while research offers the robustness which geometry lacks. New recursive designs get rid of previous regulations on suggestions passivation. Recursive Lyapunov designs for suggestions, feedforward and interlaced constructions lead to suggestions structures with optimality houses and balance margins. The design-oriented process will make this paintings a priceless device for all those that be interested on top of things conception.

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The same notation is used for vector fields in IRn . All the results are presented under the differentiability assumptions which lead to the shortest and clearest proofs. This book does not require the formalism of differential geometry and employs Lie derivatives only for notational convenience. If f : IR n → IRn is a vector field and h : IRn → IR is a scalar function, the notation Lf h is used for ∂h f (x). It is recursively extended to ∂x Lkf h(x) = Lf (Lfk−1 h(x)) = ∂ k−1 (L h)f (x) ∂x f A C 0 function γ : IR+ → IR+ is said to belong to class K, in short γ ∈ K, if it is strictly increasing and γ(0) = 0.

GS global stability CLF control Lyapunov function GAS global asymptotic stability ZSD zero-state detectability LES local exponential stability ZSO zero-state observability OFP output feedback passivity SISO single-input single-output IFP input feedforward passivity MIMO multi-input multi-output A C 0 function β : IR+ × IR+ → IR+ is said to belong to class KL if for each fixed s the function β(·, s) belongs to class K, and for each fixed r, the function β(r, ·) is decreasing and β(r, s) → 0 as s → ∞.

5) for all u ∈ U and all T ≥ 0 such that x(t) ∈ X for all t ∈ [0, T ]. The function S(x) is then called a storage function. 2 (Passivity) System H is said to be passive if it is dissipative with supply rate w(u, y) = uT y. ✷ We see that passivity is dissipativity with bilinear supply rate. In our circuit example, the storage function S is the energy, w is the input power, 28 CHAPTER 2. PASSIVITY CONCEPTS AS DESIGN TOOLS and 0T w(u(t), y(t)) dt is the energy supplied to the system from the external sources.

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Constructive Nonlinear Control by R. Sepulchre

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