By Alain Bensoussan, Jacques Louis Lions

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**Extra info for Analysis and Optimization of Systems**

**Example text**

State Let space A, system B, C,' admits and /) a be (finite-dimensional) real-valued matrices. Consider the behavioral equations ,~x=Tlx+~v, w=~x+b.. We will call this a (DV) (driving varlable)-system. (Z, Rq,~) with ~:={w~(Rq)Zl::lxe(R") z, 3re(am) z with Ilere v i,'i called drivhig varialih;. It defines the system ax=Ax+Bu, w=Cx+~)u}. 18 Finally we arrive at the familiar i n p u t - s t a t e - o u t p u t s y s t e m . Let A e R "~', B e R 'a~", C e R P~n and O e R p"" and consider the behavioral equations ax=Ax+Bu We will call this , y=Cx+Dv.

H. (1980). B. , and B. Levy assignuent Trans. Pandolfi, equations. iinear-quadratic-Gaussian control, 18. optiual Robustness systeus. controllers Control, Autom. properties Proc. and 49-75. of 2 1 s t for AC-25, of linear 528-531. linear Conference quadratic on D e c i s i o n 1267-1272. (1978). for Autom. L. the in t h e s t a t e , quadratic (1982). for and O p t i m i z a t i o n . IEEE T r a n s . W. Control Generalized systems. hereditary OIbrot, $1AN J. (1980). hereditary theory systems witb delays observations.

Is the feedback by c a l c u l a t i n g and s o l v i n g clarified the it Kuho in state and control, f o r m of a state that Second T. APPROACH - Waseda U n i v e r s i t y , problem generalized shown f i r s t condition. control quadratic given correspondingly is Shimemura, Engineering, For systems with delays linear-quadratic solution E. of E l e c t r i c a l AND PREDICTION IN STATE AND CONTROL makes control of the also functional Finally it possible a pole shifting problem witi~in the framework of the linearoptimal control problem.