Abstract
The present paper gives a procedure for determining a H∞ optimal controller in the assumption that the game Riccati equations have stabilizing positive definite solutions at the optimum value. A specific feature of the construction is its first step consisting in balancing with respect to the positive definite stabilizing solutions of the Riccati equations. The justification is based on singular perturbations reduction.
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V. Dragan, A. Halanay and A. Stoica, Remarks on order reduction for a robustly suboptimal controller via singular perturbations, Systems Control Lett. 24 (1995) 317–320.
V. Dragan, A. Halanay and A. Stoica, Two-block Nehari and H∞ problems, Preprint no. 1/1995, Institute of Mathematics of the Romanian Academy (1995).
J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, State-space solutions to standard H2 and H∞ control problems, IEEE Trans. Automat. Control 34 (1989) 831–846.
K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds, Internat. J. Control 39 (1984) 1115–1193.
K. Glover and J. Doyle, State-space formulae for all stabilizing controllers that satisfy an H∞ norm bound and relations to risk sensitivity, Systems Control Lett. 11 (1988) 167–172.
D. Hinrichsen and A.J. Pritchard, Real and complex stability radii: a survey, in: Proceedings of the International Workshop, Bremen, West Germany, June 1989 (Birkhäuser, 1990) pp. 119–164.
K. Glover, D.J.N. Limebeer, J.C. Doyle, E.M. Kasenally and M.G. Safonov, A characterization of all solutions to the four block general distance problem, SIAM J. Control Optim. 29 (1991) 283–324.
D.S. Bernstein and W.M. Haddad, LQG control with an H∞ performance bound: A Riccati equation approach, IEEE Trans. Automat. Control 34 (1989) 293–305.
P. Gahinet, Reliable Computation of H∞ central controllers near the optimum, Rapport de recherche, INRIA, no. 1642 (1992).
M.G. Safonov and D.J.N. Limebeer, Simplifying the H∞ theory via loop shifting, in: Proc. IEEE Conf. on Decision and Control, Austin, TX (December 7–9, 1988).
H. Wimmer, Monotonicity of maximal solutions of algebraic Riccati equations, Systems Control Lett. 5 (1985) 317–319.
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Dragan, V., Halanay, A. & Stoica, A. Well-conditioned computation for H ∞ controller near the optimum. Numerical Algorithms 15, 193–206 (1997). https://doi.org/10.1023/A:1019145904498
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DOI: https://doi.org/10.1023/A:1019145904498