By Alessandro Astolfi, Lorenzo Marconi
This ebook is a tribute to Prof. Alberto Isidori at the party of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact study task 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 recommendations 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 all over the world. the amount collects 27 contributions written by means of a complete of fifty two researchers. The imperative writer of every contribution has been chosen one of the - searchers who've labored with Prof. Isidori, have in?uenced his examine task, or have had the privilege and honour of being his PhD scholars. The contributions deal with a signi?cant variety of keep an eye on subject matters, together with th- retical concerns, complicated purposes, rising keep an eye on instructions and instructional works. the range of the components coated, the variety of individuals and their overseas status supply facts of the impression of Prof. Isidori within the keep watch over and structures concept groups. The e-book has been divided into six elements: process research, Optimization equipment, suggestions layout, rules, Geometric tools and Asymptotic research, re?ecting vital keep an eye on components which were strongly in- enced and, from time to time, pioneered through Prof. Isidori.
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Additional resources for Analysis and Design of Nonlinear Control Systems: In Honor of Alberto Isidori
Observe that Lemma 3 still holds when VT (r) is endowed with the Whitney topology. Hence, for each c ∈ S, there exist a neighborhood Nc of c and a neighborhood Uc ⊆ VT (r) of u such that Fc [v] ∞ > δ/2 for all c ∈ Nc , v ∈ Uc . By compactness of S, there are ﬁnitely many L L c1 , c2 , . . , cL such that S ⊆ i=1 Nci . Let U = i=1 Uci . Then U is a neighborhood of u, and for each v ∈ U , Fc [v] ∞ > δ/2 for all c ∈ S. 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 , .
W| = l if w = Xi1 Xi2 · · · Xil . Let Lm e,∞ denote the set of measurable, locally essentially bounded functions u : [0, ∞) → Rm . For each u ∈ Lm e,∞ and S0 ∈ R[[Θ]], consider the initial value problem m ˙ S(t) = X0 + Xi u i S(t), S(0) = S0 (3) i=1 seen as a diﬀerential equation over R[[Θ]]. A solution is an absolutely continuous curve, where derivative is understood coeﬃcient-wise. For any locally essentially bounded u( · ), by the Peano-Baker formula, there is always a solution in R[[Θ]] whose coeﬃcients are iterated integrals of u.
Using Corollary 1, one recovers the existence of universal inputs for analytic systems previously established in , but in a stronger form, uniformly on all state space systems of all dimensions with input functions taking values in Rm . References 1. T. Chen. Iterated path integrals. Bulletin AMS, 83:831–879, 1987. 2. M. Fliess. R´ealisation locale des syst`emes non lin´eaires, alg`ebres de Lie ﬁltr´ees transitives et s´eries g´en´eratrices non commutatives. Invent. , 71:521–537, 1983. 3. M.