By Eitan Altman, Tamer Başar, Naira Hovakimyan (auth.), Jerzy A. Filar, Vladimir Gaitsgory, Koichi Mizukami (eds.)
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Extra info for Advances in Dynamic Games and Applications
Uchida 36 then the controller (r) solving the problem [P] is given as i u = Ax - B(x)B T (x)Xx =- B T + y-2 B\ Bf Xx + TCJ (y - C2X), (x)Xx. (26) (27) Moreover, the closed-loop system (E, r) is internally stable in the maximum hyperellipsoid that is contained in the domain <1>2. 1. 1 of. 1 corresponds. This paper gives another type of controller as shown for linear systems in  and . 2. We use condition (C23) (or (C13» to obtain the largest domain possible. , in ), the higher-order terms of condition (C23) (or (C13», with respect to the state, are contained in a "gap" of the inequality (24) (or (18» and condition (C23) (or (C13» becomes useless.
The basic approach to the problem here is game-theoretic, which associates a particular differential game with the disturbance attenuation problem. Here we only consider the finite horizon case, with the extension to the infinite-horizon problem to be dealt with in another forthcoming paper. Under a 50 M Xiao and T B~ar rather weak assumption on the infinitesimal generator A (which is that A generates a Co-semigroup on X), we develop a general theory for existence and characterization of disturbance attenuating time-varying state-feedback controllers for H'~o problems in infinite dimensions.
5] Grace, A Optimization Toolbox User's Guide. The MathWorks, 1994. , T. Sugie, and T. Yoshikawa. Internal Stability and L 2 gain of Nonlinear Systems-Derivation of Bounded Real Condition. 6 659-667,1993. In Japanese.  Isidori, A. Hoo Control via Measurement Feedback for Affine Nonlinear Systems. International Journal ofRobust and Nonlinear Control, 4, 553-574, 1994.  Ito, K. and T. Tsuji. The Bilinear Characteristics of Muscle-Skeletomotor System and the Application to Prosthesis Control.