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Analysis and design of nonlinear control systems : in honor by Alessandro Astolfi, Lorenzo Marconi

By Alessandro Astolfi, Lorenzo Marconi

This publication is a tribute to Prof. Alberto Isidori at the celebration of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact learn task has spanned over 35 years. all through his profession, Prof. Isidori has constructed ground-breaking effects, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his commitment to provide an explanation for elaborate concerns and di?cult ideas 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 through a complete of fifty two researchers. The primary 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 tackle a signi?cant variety of regulate issues, together with th- retical concerns, complex functions, rising regulate instructions and educational works. the variety of the parts coated, the variety of individuals and their foreign status supply proof of the effect of Prof. Isidori within the keep watch over and platforms concept groups. The booklet has been divided into six components: process research, Optimization tools, suggestions layout, law, Geometric tools and Asymptotic research, re?ecting very important regulate components which were strongly in- enced and, often times, pioneered via Prof. Isidori.

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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.

Systems & Control Letters, 5(1):41–47, 1984. D. Sontag and Y. Wang 10. D. Sontag. Universal nonsingular controls. Systems & Control Letters, 19(3):221–224, 1992. 11. D. Sontag. Spaces of observables in nonlinear control. Proceedings of the International Congress of Mathematicians, 1:1532–1545, 1994. 12. D. Sontag. Control of systems without drift via generic loops. IEEE Trans. on Automat. , 40(7):1210–1219, 1995. 13. D. Sontag. Mathematical Control Theory: Deterministic Finite Dimensional Systems.

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. We say p and q are distinguished by u, denoted by p ∼u q, if h(ϕ( · , p, u)) = h(ϕ( · , q, u)) (considered as functions defined on the common domain of ϕ( · , p, u) and ϕ( · , q, u)); otherwise we say p and q cannot be distinguished by u, denoted by p ∼u q.

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