By Alain Bensoussan, Jacques Louis Lions

ISBN-10: 0387167293

ISBN-13: 9780387167299

Textual content: English, French

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53-57, 1978. R. Barmish, "Invariance of the strict Hurwitz property for polynomials with perturbed coefficients," tEEE Trans. Automat. , vol. AC-29, no. 10, pp. 935-936, I984. [5] S. Bialas and J. Garloff, "Stability of polynomials under coefficient perturbations," IEEE Trans. Automat. , vol. AC-30, no. 3, pp. 310-312, 1985. B. Argoun, "Frequency domain conditions for the stability of perturbed polynomials," IEEE Trans. Automat. , vol. AC-32, no. 10, pp. 913-916, Oct. 1087. M. Biernacki, H. P. Bhattacharyya, "Robust stability with structured real parameter perturbations," 1EEE Trans.

Matrix (h)B~. Note ~ = • that state the result. Theorem the 2. Assume unstable zeros characteristic triplet Qe : *'(0)0* is xP ' ( u and the = V '(0)P~ (0) P, C B ) = • '(0)PV B ) = V '(a a non-negative where Riccati P is tilt: Cs) (l) is with stabilizable non-negative Then, = O. QI,Q~} O,(B) that + Q - PiCA R - t B ~ (11) in T h e o r e m provides I. the P = 0. optimal C12) regulator having the properties 39 Proof. See A p p e n d i x 2. We o b s e r v e h e r e that is decomposed into First note optimal that, : control law g i v e n by t h e s o l u t i o n the s p e c t r u m d e c o m p o s i t i o n from t h e p a r t i c u l a r control u(t) the optimal law (6) is " R ' ' { ~ (0)B~ part structure rewritten (I1) and t h e p r e d l , ' t i o n of t h e s o l u t i o n (li).

Field a special the matrix. $~(a. t o be i n t e r p r e t e d defined B ) for ( @ e . @ ~ ) Is D e n o t e by not ones being is shown t h a t for which number of o p e n Riccati equation and p r e d i c t i o n functional the part: makes it framework of the the space = 52(B, {Se,S~,S~}, as f o l l o w s , is the LQ with square as a ), the (row) of s q u a r e integrable v and m a t r i x their {$e,SI,S~} In Rnxn, short Is is the L ~ ( [ a , b ] : R ~) and as t h e c o m p l e x of a m a t r i x $1 and in L ~ ( [ - b , O ] ; R n~n) and $~ is called - h ~ a ~ O.

### Analysis and Optimization of Systems by Alain Bensoussan, Jacques Louis Lions

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