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Discrete time \({\mathcal H}_\infty\) controllers satisfying a minimum entropy criterion. (English) Zbl 0701.93027

Summary: A discrete time, minimum entropy \({\mathcal H}_{\infty}\) control problem is solved and state space formulae are derived. The solution is obtained from this principles and so avoids the reformulation of the problem to a continuous time problem via a bilinear transformation.

MSC:

93B36 \(H^\infty\)-control
93B35 Sensitivity (robustness)
93C55 Discrete-time control/observation systems
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[1] Arov, D.Z.; Krein, M.G., On the evaluation of entropy functionals and their minima in generalized extension problems, Acta sci. math., 45, 33-50, (1983), In Russian · Zbl 0556.47013
[2] Arov, D.Z.; Krein, M.G., Problem of search of the minimum entropy in indeterminate extension problems, Functional analysis and its applications, 15, 123-126, (1981) · Zbl 0484.46060
[3] Ball, J.A.; Ran, A.C.M., Optimal Hankel norm model reductions and Wiener-Hopf factorization I: the canonical case, SIAM J. control optim., 25, 362-382, (1987) · Zbl 0623.93016
[4] Dym, H., J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, (1988), CBMS Lecture
[5] Francis, B.A., A course in \(H\)_{∞} control theory, ()
[6] Glover, K., All optimal Hankel-norm approximations of linear multivariable systems and their \(L\)_{∞}-error bounds, Internat. J. control, 39, 1115-1193, (1984) · Zbl 0543.93036
[7] Glover, K.; Limebeer, D.; Doyle, J.; Kasenally, E.; Safonov, M., A characterization of all solutions to the four block general distance problem, SIAM J. control optim., (1990), to appear
[8] Glover, K.; Mustafa, D., Derivation of the maximum entropy \(H\)_{∞}-controller and a state-space formula for its entropy, Internat. J. control, 50, 899-916, (1989) · Zbl 0681.93028
[9] Gohberg, I.; Kaashoek, M.A.; van Schagen, F., Rational contractive and unitary interpolants in realized form, Integral and operator theory, 11, 105-127, (1988) · Zbl 0649.47016
[10] Mustafa, D., Relations between maximum entropy/\(H\)_{∞} control and combined \(H\)∞/LQG control, Systems control lett., 12, 193-203, (1989) · Zbl 0673.93090
[11] Mustafa, D.; Glover, K., Controllers which satisfy a closed-loop \(H\)_{∞} norm bound and maximize an entropy integral, ()
[12] Rudin, W., Real and complex analysis, (1966), McGraw-Hill New York · Zbl 0148.02904
[13] Young, N., An introduction to Hilbert space, (1988), Cambridge University Press Cambridge · Zbl 0645.46024
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