Abstract
In the present paper, a new set of necessary and sufficient conditions is given for the regulator problem with plant stability in the presence of disturbances. Significant features of these conditions are the simplicity of their statement and the immediacy of their meaning in the context of the geometric approach. The proof is based on arguments which are extensions of those developed in Part 1 for the more restricted problem of disturbance localization by dynamic compensation with stability. The sufficiency of conditions is proved by a constructive procedure, which may be used as part of an actual regulator synthesis method.
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Bhattacharyya, S. P., Pearson, J. B., andWonham, W. M.,On Zeroing the Output of a Linear System, Information and Control, Vol. 20, pp. 135–142, 1972.
Wonham, W. M.,Tracking and Regulation in Linear Multivariable Systems, SIAM Journal on Control, Vol. 11, pp. 424–437, 1973.
Wonham, W. H., andPearson, J. B.,Regulation and Internal Stabilization in Linear Multivariable Systems, SIAM Journal on Control, Vol. 12, pp. 5–18, 1974.
Anderson, B. D. O.,Output Nulling Invariant and Controllability Subspaces, Proceedings of the 6th IFAC World Congress, 1975.
Francis, B. A.,The Linear Multivariable Regulator Problem, SIAM Journal on Control and Optimization, Vol. 15, pp. 486–505, 1977.
Schumacher, J. M. H.,Regulator Synthesis Using (C, A, B)-Pairs, IEEE Transactions on Automatic Control, Vol. AC-27, pp. 1211–1221, 1982.
Basile, G., andMarro, G.,Self-Bounded Controlled Invariants versus Stabilizability, Journal of Optimization Theory and Applications, Vol. 48, pp. 245–263, 1986.
Basile, G., Marro, G., andPiazzi, A.,Stability without Eigenspaces in the Geometric Approach: Some New Results, Proceedings of the 7th International Symposium on the Mathematical Theory of Networks and Systems, Stockholm, Sweden, 1985.
Imai, H., andAkashi, H.,Disturbance Localization and Pole Shifting by Dynamic Compensation, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 226–234, 1981.
Willems, J. C., andCommault, C.,Disturbance Decoupling by Measurement Feedback with Stability or Pole Placement, SIAM Journal on Control and Optimization, Vol. 19, pp. 490–540, 1981.
Basile, G., Marro, G., andPiazzi, A.,A New Constructive Geometric Solution to the Regulator Problem with Disturbances under the Plant Stability Constraint (to appear).
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Communicated by G. Leitmann
This research has been supported in part by MPI, Rome, Italy.
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Basile, G., Marro, G. & Piazzi, A. Revisiting the regulator problem in the geometric approach, part 2, asymptotic tracking and regulation in the presence of disturbances. J Optim Theory Appl 53, 23–36 (1987). https://doi.org/10.1007/BF00938814
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DOI: https://doi.org/10.1007/BF00938814