## A linear matrix inequality approach to $$H_ \infty$$ control.(English)Zbl 0808.93024

### MSC:

 93B36 $$H^\infty$$-control 93B50 Synthesis problems 93B51 Design techniques (robust design, computer-aided design, etc.) 93B52 Feedback control 93C80 Frequency-response methods in control theory
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### References:

 [1] Bernstein, IEEE Trans. Automatic Control AC-34 pp 293– (1989) [2] Boyd, Lin. Alg. & Applic. 188 pp 63– (1993) [3] and , ’A generalized eigenproblem solution for singular H2 and H problems’ in Control and Dynamic Systems, vol. 50, (Ed.), Academic Press, New York, 1992. [4] ’A note on the analyticity of the Riccati metric’, in Algebraic and Geometric Methods in Linear Systems Theory, Lecture Notes in Applied Mathematics 18, Amer. Math. Soc., Providence, RI, 1980, pp. 37–41. [5] Doyle, IEEE Trans. Automatic Control. AC-34 pp 831– (1989) [6] and , ’Review of LFTs, LMIs, and ??’, Proc. CDC, 1227–1232 (1991). [7] ’Reliable computation of H central controllers near the optimum’, Proc. Amer. Contr. Conf., pp. 738–742, 1992. [8] ’On the game Riccati equations arising in H control problems’, SIAM J. Contr. Opt., May 1994. [9] ’A convex parametrization of H suboptimal controllers’, Proc. CDC, Dec. 1992, pp. 937–942. Also in INRIA Technical Report #1712. [10] Gahinet, Proc. European Contr. Conf. (1993) [11] Glover, Syst. Contr. Letters 11 pp 167– (1988) [12] and , ’A complete solution to the general H control problem: LMI existence conditions and state-space formulas’, submitted to Automatica, October 1992. [13] Laub, IEEE Trans. Automatic Control. AC-24 pp 913– (1979) [14] and , Interior Point Polynomial Methods in Convex Programming: Theory and Applications, SIAM publications, to appear in 1993. [15] , and , ’A collection of robust control problems leading to LMI’s’, Proc. CDC, 1245–1250 (1991). [16] Peterson, Int. J. of Robust and Nonlinear Control 1 pp 171– (1991) [17] ’The Riccati inequality and state-space H-optimal control’, Ph.D. Dissertation, Universitat Wurzburg, Germany, 1990. [18] Scherer, SIAM J. Contr. Opt. 30 pp 143– (1992) [19] Sefton, Syst. Contr. Letters 14 pp 295– (1990) [20] Stoorvogel, SIAM J. Contr. Opt. 29 pp 160– (1991) [21] and , ’A reduced-order observer-based controller design for H optimization’, Proc. AIAA Guidance, Navigation and Control Conf., 1991. [22] The H Control Problem: a State-Space Approach, Prentice Hall, Hemel Hempstead, UK, 1992. [23] and , ’Pole-zero cancellations and closed-loop properties of an H mixed-sensitivity design problem’, Proc. CDC, 1028–1029 (1990).
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