By Laura Menini, Luca Zaccarian, Chaouki T. Abdallah

This quantity is an outgrowth of the workshop "Applications of complex keep an eye on concept to Robotics and Automation, "organized in honor of the seventieth birthdays of Petar V. Kokotovic and Salvatore (Turi) Nicosia. either Petar and Turi have performed unique paintings within the keep an eye on neighborhood and feature lengthy been well-known as mentors, in addition to specialists and pioneers within the box of automated keep watch over, overlaying many themes on top of things thought and a number of other diverse purposes. the diversity in their examine is mirrored during this ebook, which include contributions starting from arithmetic to laboratory experiments.

The scope of the paintings is especially vast, and even supposing every one bankruptcy is self-contained, the booklet has been prepared into thematically similar chapters, which now and again, recommend to the reader a handy examining series. the nice number of subject matters coated and the virtually educational writing type utilized by a number of the authors will make this publication appropriate for either specialists within the regulate box and younger researchers who search a extra intuitive realizing of those suitable issues within the field.

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Additional info for Current Trends in Nonlinear Systems and Control: In Honor of Petar Kokotovic and Turi Nicosia (Systems & Control: Foundations & Applications)

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The submodule S is said closed in T (or simply closed) if S = S T . We can easily prove that dim S = dim S and that S is the smallest closed submodule containing S. A key result concerning closed submodules over a PID R is the following. Proposition 2. ([5]) Let R be a PID. , there exists a submodule W ⊆ T such that T = S ⊕ W; iii) any basis of S can be completed to a basis of T . UIO and RG problems 21 A consequence of Proposition 2 and the fact that submodules of a free module over a PID are free (that is, isomorphic to Rq for some q) is that the quotient module T /S, when S is closed in T , is also free.

5 The RG problem Let us consider now the linear, time invariant, delay-differential, dynamical system Σd be described by the set of equations ⎧ a b x˙ (t) = i=0 Ai x (t − ih) + i=0 Bi u(t − ih)+ ⎪ ⎪ ⎨ l1 ls 1 Lsi ms (t − ih) + i=0 Li m1 (t − ih) + · · · i=0 (11) ⎪ ⎪ ⎩ c y(t) = i=0 Ci x (t − ih), where u is the control input, mj belongs to the so-called failure input space Mj = Rmj , j = 1, . . , s, and Lji , j = 1, . . , r, i = 1, . . , lj are matrices of suitable dimensions with entries in R.

S, and Lji , j = 1, . . , r, i = 1, . . , lj are matrices of suitable dimensions with entries in R. The occurrence of a nonzero input mj ∈ Mj represents a failure that has to be detected and recognized. This motivates the interest in constructing, if possible, a system ΣRGd that, having as input the control input of Σd and its output, generates an output r(t) that is essentially influenced only by the failure input mj for each specific j = 1, . . , s. Such a system is called a residual generator and its output is called a residual output (see [15]).

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