System Theory

Download Analysis and Design of Nonlinear Control Systems: In Honor by Alessandro Astolfi, Lorenzo Marconi PDF

By Alessandro Astolfi, Lorenzo Marconi

This ebook is a tribute to Prof. Alberto Isidori at the celebration of his sixty fifth birthday. Prof. Isidori’s proli?c, pioneering and high-impact examine job has spanned over 35 years. all through his profession, Prof. Isidori has built ground-breaking effects, has initiated researchdirections and has contributed towardsthe foundationofnonlinear controltheory.In addition,his commitment to give an explanation for complicated concerns and di?cult strategies in an easy and rigorous means and to inspire younger researchers has been instrumental to the highbrow development of the nonlinear regulate neighborhood around the world. the amount collects 27 contributions written by way of a complete of fifty two researchers. The significant writer of every contribution has been chosen one of the - searchers who've labored with Prof. Isidori, have in?uenced his examine job, or have had the privilege and honour of being his PhD scholars. The contributions tackle a signi?cant variety of keep watch over subject matters, together with th- retical matters, complicated purposes, rising keep watch over instructions and educational works. the variety of the components lined, the variety of members and their foreign status supply proof of the influence of Prof. Isidori within the keep an eye on and structures concept groups. The e-book has been divided into six elements: method research, Optimization tools, suggestions layout, legislation, Geometric tools and Asymptotic research, re?ecting very important keep watch over components which were strongly in- enced and, every so often, pioneered by way of Prof. Isidori.

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Example text

This shows the density property of ΩST . To show the openness property of ΩST , let u ∈ ΩST . By definition, for any c ∈ S, there exists some tc ∈ [0, T0 ] such that Fc [u](tc ) = 0, so uT0 ∈ ΩST0 . By openness of ΩST0 , there is a neighborhood U of uT0 in C ∞ [0, T0 ] such that uT0 ∈ U ⊆ ΩST0 . Let ˜ = {v ∈ C ∞ [0, T ] : v ∈ U }. U T0 ˜ is a neighborhood of u in C ∞ [0, T ], and U ˜ ⊆ Ω T . This shows that Then U S T T every u in ΩS is an interior element of ΩS . Uniformly Universal Inputs 21 Proof of Lemma 6.

It is important to incorporate these auxiliary variables in our modeling language ab initio, and to distinguish clearly between the variables whose behavior the model aims at, and the auxiliary variables introduced in the modeling process. The former are called manifest variables and the latter latent variables. A mathematical model with latent variables is defined as a triple (U, L, Bfull ), with U the universum of manifest variables, L the universum of latent variables, and Bfull ⊆ U × L the full behavior .

The same proof can be used to prove the following result for equi-convergent families. Uniformly Universal Inputs 15 Lemma 2. Assume that S is equi-convergent, and (T, r) is admissible for S. Then the map VT (r) → C[0, T ], u → Fc [u] is continuous with respect to the L1 norm on VT (r) and the C 0 norm on C[0, T ] uniformly for c ∈ S. ✷ This result can be strengthened further to the following, where the topology on VT (r) is the L1 -topology, and the topology on C[0, T ] is the C 0 topology. Lemma 3.

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