Modeling and Control of Economic Systems 2001. A Proceedings by R. Neck

By R. Neck

This quantity comprises papers provided on the IFAC symposium on Modeling and keep watch over of financial platforms (SME 2001), which used to be held on the collage of Klagenfurt, Austria. The symposium introduced jointly scientists and clients to discover present theoretical advancements of modeling suggestions for fiscal platforms. It incorporates a part of plenary, invited and contributed papers offered on the SME 2001 symposium. The Read more...

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Modeling and Control of Economic Systems 2001. A Proceedings volume from the 10th IFAC Symposium, Klagenfurt, Austria, 6 – 8 September 2001

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Additional info for Modeling and Control of Economic Systems 2001. A Proceedings volume from the 10th IFAC Symposium, Klagenfurt, Austria, 6 – 8 September 2001

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Again we restrict ourselves to the purely quadratic case. Z "- j e (A+BF)Tt e ( A + B F ) t dt - Z T 0 fulfills 0 < Z < p2I and so Z solves the Lyapunov equation (A + B F ) T Z + Z ( A + B F ) + I - Theorem 11. Let f~ be an LQ-game. f't is playable if and only if the following conditions hold: 0 and that shows in fact that A + B F must be stable. It remains to show that the boundary value problem (7) admits exactly one solution. e. e. (x x~ , A~~, A~~ With the transformation of variables: (x) (, o o)(x) Aa /~1 - K1 K2 I 0 0 I pl #2 (1) Rii > 0 f o r i - - - 1,2.

T. D Note that if the matrices Q i and Rij are positive semidefinite, the inequalities in Y/ are trivially satisfied The generalization of theorem 7 is then 27 for < all n Theorem 9 Assume there exist N real symmetric matrices X~ > 0 satisfying Qi + A T x i + X i A + x3s REFERENCES Ba~ar, T. J. Olsder (1999). Dynamic Noncooperative Game Theory. SIAM, Philadelphia. Ba~ar, T. and P. Bernhard (1995). Ha-Optimal Con- Ej]v~i(XiSjX j -~- XjSjA'i) jxj + "y;- X EETX - O; trol and Related Minimax Design Problems.

Dynamic Noncooperative Game Theory. SIAM, Philadelphia. Ba~ar, T. and P. Bernhard (1995). Ha-Optimal Con- Ej]v~i(XiSjX j -~- XjSjA'i) jxj + "y;- X EETX - O; trol and Related Minimax Design Problems. A,i "- A - E j ~ I S j X j + 7~ 2EE TXi is stable, i r N Birkh~iuser, Boston. A. van den (2001). Uncertainty in Differential Games, PhD. Thesis, CentER Dissertation Series, Tilburg University, The Netherlands, ISBN 90-5668-081-1. A. (1987). 88. Springer-Verlag, Berlin. Glover, K. C. Doyle (1988). State-space formalae for all stabilizing controllers that satisfy an H ~ norm bound and relations to risk sensitivity.

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