Download e-book for iPad: Control of Uncertain Systems with Bounded Inputs by Sophie Tarbouriech, Germain Garcia

By Sophie Tarbouriech, Germain Garcia

In useful regulate difficulties, many constraints must be dealt with so one can layout controllers which function in a true atmosphere. through combining effects on strong keep an eye on and saturating keep watch over, this publication makes an attempt to supply optimistic support for sensible occasions and, as one of many first books to merge the 2 regulate fields, it may generate substantial curiosity in scientific/acad emic circles. the 10 chapters, which care for stabilization and keep watch over of either linear and nonlinear platforms, are each one self sufficient of their technique - a few deal in basic terms with theoretical effects while others pay attention to ways that the speculation will be utilized. The book's solidarity is secured through the will to formulate keep watch over layout standards via constraints on enter and version uncertainty description.

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We have XI -'~ ALIa1 + AI,IIXlI ~U=0 where AI,I and AI,II are appropriate submatrices of A. For i E { 1 , . . , k } , l e t d~ = 1 - I z i ( t o ) [ . For i E { k + l , . . , l}, there exists di > 0 such that (7~7= 1 aa(i)jzj)zo(i)(to) < 0, for all x such [Ix - a(t0)]] < Hi. 1). Then, Ixi(t)] is strictly decreasing and it must be true that [xi(t)[ < 1 for all t E (to,to + r). For i E { l + l , . - . , m}, consider the second-order right derivative of zi with respect to t, d2 d '~ -~-~ai = "~ E aijxj = [hi1,'", a~l](AI,IzI + AI,IIaH).

Press, Princeton NJ (1971). 22. S. Skogestad, M. Morari and J. Doyle, Robust Control of Ill-Conditioned Plants: High-Purity Distillation, IEEE Trans. Autom. , 33, 12, (1988) 1092-1105. 23. A. Sideris and H. Rotstein, Single Input-Single Output 7/ΒΆΒΆ Control with Time Domain Constraints, Automatica, 29, 4, (1993) 969-984. 24. D. J. Sussmann, Nonlinear output feedback design for linear systems with saturating controls, Proc. 29th. , (1990) 3414-3416. 25. R. SuArez, J. Alvarez, and J. Alvarez, Regions of Attraction of Closed Loop Linear Systems with Saturated Linear Feedback Journal of Math.

7) becomes m a x . 8) where v is the row dimension of the matrix S(F, w) This last condition is obviously useful if we want to characterize the invariance of some set with respect to a dynamical systems, with uncertain matrix A. 3. [S(M,s) (2) - S(M,s)O)](Fd() ' < pS(M,s)(4)wi i = 1 . . 2 to check the inclusion K,U* C U. 2. e. searching for a matrix K such that in the case of nominal system (lr = 0) the contractivity factor )~ is assured and in the case of rr # 0 the contractivity factor is k', I < A' < 1.

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