This reply is concerned with a comment by Turner and Chun on the solution of the matrix Riccati equation used in Ref. 1. Whereas the technique suggested by Turner and Chun may have some numerical advantage over Potter's method in the case of coupled large-order systems, the advantage is minimal when the independent modal-space control method is used.
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Öz, H., andMeirovitch, L.,Stochastic Independent Modal-Space Control of Distributed Parameter Systems, Journal of Optimization Theory and Applications, Vol. 40, pp. 121–154, 1983.
Potter, J. E.,Matrix Quadratic Solutions, SIAM Journal on Applied Mathematics, Vol. 14, pp. 496–501, 1966.
Öz, H., andMeirovitch, L.,Optimal Modal-Space Control of Flexible Gyroscopic Systems, Journal of Guidance and Control, Vol. 3, pp. 218–226, 1980.
Turner, J. D., andChun, H. M.,Stochastic Independent Modal-Space Control of Distributed-Parameter Systems (Technical Comment), Journal of Optimization Theory and Applications, Vol. 44, pp. 181–185, 1984.
Kreider, D. L., Kuller, R. D., Ostberg, D. R., andPerkins, F. W.,An Introduction to Linear Analysis, Addison-Wesley, Reading, Massachusetts, 1966.
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Öz, H., Meirovitch, L. Stochastic independent modal-space control of distributed-parameter systems. J Optim Theory Appl 44, 187–188 (1984). https://doi.org/10.1007/BF00934901
- Stochastic estimation and control
- independent modal-space control
- distributed-parameter systems
- Potter's method
- matrix Riccati equation
- transition matrix