By Alessandro Astolfi, Lorenzo Marconi

ISBN-10: 354074357X

ISBN-13: 9783540743576

ISBN-10: 3540743588

ISBN-13: 9783540743583

This e-book is a tribute to Prof. Alberto Isidori at the get together of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact examine job has spanned over 35 years. all through his occupation, Prof. Isidori has built ground-breaking effects, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his commitment to provide an explanation for tricky concerns and di?cult strategies in an easy and rigorous means and to encourage younger researchers has been instrumental to the highbrow progress of the nonlinear keep watch over neighborhood around the world. the amount collects 27 contributions written by means of a complete of fifty two researchers. The vital writer of every contribution has been chosen one of the - searchers who've labored with Prof. Isidori, have in?uenced his study job, or have had the privilege and honour of being his PhD scholars. The contributions deal with a signi?cant variety of regulate subject matters, together with th- retical concerns, complex purposes, rising keep an eye on instructions and educational works. the variety of the parts coated, the variety of participants and their overseas status offer proof of the influence of Prof. Isidori within the regulate and platforms idea groups. The publication has been divided into six elements: process research, Optimization tools, suggestions layout, law, Geometric tools and Asymptotic research, re?ecting vital regulate components which were strongly in- enced and, often times, pioneered via Prof. Isidori.

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**Additional info for Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori**

**Sample text**

Hence, for any c ∈ S, there exists some tc ∈ [0, T ] such that |Fc [v](tc )| = τc > 0. f. Lemma 2), there exists a neighborhood Nc of c such that for any d ∈ Nc ∩ S, Uniformly Universal Inputs 17 |Fd [v](tc )| ≥ τc /2 . n Since S is compact, there exist c1 , c2 , . . , cn such that S ⊆ i=1 Nci . It then follows that for any d ∈ S, there exists some 1 ≤ j ≤ n such that |Fd [v](tj )| ≥ τcj /2 , (15) where tj = tcj . Let μ = (μ0 , μ1 , . . , μk−1 ) ∈ Rmk be given. Let {ωj } be a sequence of analytic functions deﬁned on [0, T ] such that • • • (i) ωj (0) = μi for 0 ≤ i ≤ k − 1, j ≥ 1; ωj → v in the L1 norm (as functions deﬁned on [0, T ]); and for some M ≥ 1, ωj ∞ ≤ M for all j ≥ 1.

It follows that U ⊆ ΩST . D. Sontag and Y. Wang where for each t, x(t) ∈ M, which is an analytic (second countable) manifold of dimension n, h : M −→ R is an analytic function, and g0 , g1 , . . , gm are analytic vector ﬁelds deﬁned on M. Inputs are measurable essentially bounded maps u : [0, T ] −→ Rm deﬁned on [0, T ] for suitable choices of T > 0. In general, ϕ(t, x, u) denotes the state trajectory of (21) corresponding to an input u and initial state x, deﬁned at least for small t. Fix any two states p, q ∈ M and take an input u.

Note that every extension ν of ν N is in JS as well as in W since it is also an extension of μj . Hence, W JS = ∅. We now prove the openness property of JS . Pick μ = (μ0 , μ1 , . ) ∈ JS . Then for each c ∈ S, there exists some k ≥ 0 such that c, dk (μ) k = 0. (20) By compactness of S, one can assume that k does not depend on c. Note that (20) involves only ﬁnitely many terms, so there are neighborhoods Nc of c ∈ S and Uc,μk of μk in Rmk (where μk = (μ0 , . . D. Sontag and Y. Wang d, dk (ν) k =0 for all d ∈ Nc and all ν ∈ Uc,μk .

### Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori by Alessandro Astolfi, Lorenzo Marconi

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