Current Trends in Nonlinear Systems and Control: In Honor of by Laura Menini, Luca Zaccarian, Chaouki T. Abdallah

By Laura Menini, Luca Zaccarian, Chaouki T. Abdallah

This quantity is an outgrowth of the workshop "Applications of complicated keep an eye on thought 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 amazing paintings within the keep an eye on neighborhood and feature lengthy been famous as mentors, in addition to specialists and pioneers within the box of computerized keep watch over, protecting many subject matters up to speed thought and a number of other varied functions. the range in their examine is mirrored during this booklet, inclusive of contributions starting from arithmetic to laboratory experiments.

The scope of the paintings is especially huge, and even though each one bankruptcy is self-contained, the booklet has been equipped into thematically similar chapters, which now and again, recommend to the reader a handy interpreting series. the good number of themes lined and the just about educational writing variety utilized by some of the authors will make this publication appropriate for either specialists within the keep watch over box and younger researchers who search a extra intuitive figuring out of those proper subject matters within the field.

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40th IEEE CDC, Orlando, FL 11. Sename O, Fattouh A, Dion JM (2001) Further results on unknown input observers design for time-delay systems, Proc. 40th IEEE CDC, Orlando, FL 12. Kamen EW (1991) Linear system over rings: from R. E. Kalman to the present, Mathematical System Theory–The Influence of R. E. Kalman, Springer-Verlag, Berlin 13. Ito N, Schmale W, Wimmer HK (2000) (C,A)-invariance of modules over principal ideal domains, SIAM Journal on Control and Optimization 38(6):1859–1873 14. Lang S (1984) Algebra, Addison-Wesley, Reading, MA 15.

0001 If, for instance, L1 is such that (V ∗ +S ∗ ) (Im L1 ) = 0 holds, we can construct an observer system of the form (14) choosing G as 32 G. Conte and A. M. Perdon ⎡ γ11 ⎢ γ21 G=⎢ ⎣ γ31 γ41 γ12 γ22 γ32 γ42 ⎤ 0 0 ⎥ ⎥. 0 ⎦ γ43 Remark that, since the elements of GC must belong to R[∆], ϕ(∆) = 1. 100 Letting H = , we get the residual generator 010 ΣRG = ˜ w(t) ˙ = Kw(t) + Gy(t) ˜ r(t) = w(t) + Hy(t), where K := A11 = γ12 p1 (∆) + γ11 , γ21 p2 (∆) + γ22 ˜ := −P G, H ˜ = −H. If we take, for instance, γ12 = γ21 = 0, γ11 = −1−p1 (∆) G and γ22 = −1 − p2 (∆), ΣRG solves the FPRG for Σ.

As shown in [2], condition (48) can be removed if, in the certaintyequivalence design, the measured states are incorporated directly and not replaced with their observer estimates; that is, with the controller u = α(y, x ˆ2 ) in the coordinates of Section 5, rather than with u = α(ˆ x) = α(ˆ y, x ˆ2 ). The main assumption of Proposition 3 on the state-feedback controller is that the closed-loop system admit a Lyapunov function with a bounded gradient. Even when an available Lyapunov function does not satisfy this assumption, it may do so when scaled by a scalar nonlinear function.

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