[email protected] Alberto Isidori was born in Rapallo, Italy, in dei Sistemi (in italian), with i, ; Sistemi di Controllo (in italian). Selected publications of Alberto Isidori. Books. [1] A. Isidori, Sistemi di Controllo ( in Italian), Siderea, [2] A. Ruberti and A. Isidori, Teoria dei Sistemi (in. In Honor of Alberto Isidori Alessandro Astolfi, Lorenzo Marconi Alberto. Isidori. Books [1] A. Isidori, Sistemi di Controllo (in Italian), Siderea, [2] A. Ruberti.

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Thus we see that when A is diagonal withunrepeated eigenvalues the Jacobian of the map is diagonal with nonzeroeigenvalues. We now prove that the B Fas F varies over Tjare pairwise disjoint. T W are possible, accordingto the model: In the cnotrollo of linear systems this approachmay lead to eective algorithms based on ellipsoidal techniques which alsoallow to accurately approximate nonconvex reach sets through unions of el-lipsoids.

We begin by establishing some properties of a family of t-parametrizedcurves associated with a special case of ete H t, for which H is zero onthe diagonal.

A concept of local observability. The third part Feedback Design comprises six contributions.

Then let T be a triangulation of k that renes Winthe sense that every closed face F of T is a subset of Wx for some x. The structureof the cost, Controllkthen becomes identical to that in the problem for the Nthstage, and the quantizer in the N 1 th stage is also memoryless. Willemssystems using Lagrangians, modeling of usidori circuits using ports insteadof terminals, ieidori. Thisimplies that xr t and u t are continuous. In he was elected Fellow member of the IEEE “for fundamental contributions to nonlinear control theory”.

However, forthe unstable case, if one uses xed-length encoding, there does not exist aninvariant density for the state. Fix any two states p, q M and take an input u.

We are thankful to Sean Meyn for various insightful discussionson the topic of and results presented in this chapter. Brocketthas two distinct negative eigenvalues it does not have a real logarithm. To prove this theorem we need several lemmas. Modeling the subsystem then again involves tearing,zooming, isicori linking. Clearly, J Jand hence, the following is an immediateconsequence of Theorem 2.

Uniform scalar quantizers, inaddition to their simplicity, are also approximately optimal in the limit ofhigh-rate distortion [8] with respect to the mean-square distortion measure. Let Lme, denote the set of measurable, locally essentially bounded func-tions u: Thisshows that there is isidor uniformly universal input which is analytic.

We now passto upper controllk for V t,x and internal estimates for W t. This modeling process is called tearing, zooming, and linking. Markov Chains and Stochastic Stability. Coding for control of non-linear systems hasbeen studied by Isidori and De Qlberto [6] among others. This canbe alleviated by the partial elimination of latent variables when possible.

Input normal form of degree d is similar to a normal form of Scherpen [12].

### Alberto Isidori

Isidori, Robust global stabilization of a class of uncertainfeedforward nonlinear systems, Systems and Control Lett. Reducing thevalue of T if necessary, one may assume that T,M is admissible for alld S. The rst lemma is on a one-to-one mapping between the trajectory sets of 9 and 2.

Nonlinear target control 85Theorem 5. Products of positive denite matrices. Dynamic Programming and Optimal Control. Isidori received the Georgio Quazza Medal. He has also served in the program committee of several jsidori international Conferences. One can go a certain distance withthis map idea in the context of linear systems, say by assuming both theinput and the output to be zero in the far past, or by restricting to squareintegrable inputs and outputs.

Six contributions compose the fourth part Regulation. A rst principles model of an interconnected system obtained thisway always contains many latent variables. We will actually prove siztemi result for a general smooth singular subbundleE of an arbitrary smooth vector bundle V over a smooth manifold M.

The following facts are more or less immediate. This decompositionis often more useful than the familiar polar form. Throughout his career, Prof.

## Analysis and Design of Nonlinear Control Systems ||

Theschemes for verifying the desired properties will usually consist in checkingsome inequalities or solving some optimization problems over respective valuefunctions or their approximations. This tearing-zooming-linking modeling methodology has many virtues: For both of us, theencounter ri Prof. In order to discover theseinteractions, we look inside the blackbox of Figure 3, where we nd an inter-connection architecture alberfo smaller blackboxes that interact through terminalsof their own see Figure 4.

For such T, rwe say that T, r is admissible for S. A mathematical model with latent variables is dened as a triple U,L,Bfull ,with U the universum of manifest variables, L the universum of latent vari-ables, and Bfull U L the full behavior. Isidori, Global almost disturbance decoupling with stability xi non-minimum phase single-input single-output nonlinear systems, Systems andControl Lett.