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Anderson, B. D. O.

Publications and source records attributed to Anderson, B. D. O..

4 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Output feedback and generic stabilizability

Attention is given to questions of pole placement and stabilization for generic linear systems with prescribed state, input and output dimension for the case where the controller must be implemented by linear memoryless output feedback. A criterion is presented in terms of a special pole placement property for generic stabilizability, and this criterion is used to describe constraints on the dimension which are consistent with generic stabilizability. Also treated are the rationality and solvability by radicals of stabilizing or pole positioning gains, and the way in which decision algebra can theoretically handle existence questions for generic systems is described.

Byrnes, C. I.↗
NASA NTRS1983

On the stabilizability of multivariable systems by minimum order compensation

In this paper, a derivation is provided of the necessary condition, mp equal to or greater than n, for stabilizability by constant gain feedback of the generic degree n, p x m system. This follows from another of the main results, which asserts that generic stabilizability is equivalent to generic solvability of a deadbeat control problem, provided mp equal to or less than n. Taken together, these conclusions make it possible to make some sharp statements concerning minimum order stabilization. The techniques are primarily drawn from decision algebra and classical algebraic geometry and have additional consequences for problems of stabilizability and pole-assignability. Among these are the decidability (by a Sturm test) of the equivalence of generic pole-assignability and generic stabilizability, the semi-algebraic nature of the minimum order, q, of a stabilizing compensator, and the nonexistence of formulae involving rational operations and extraction of square roots for pole-assigning gains when they exist, answering in the negative a question raised by Anderson, Bose, and Jury (1975).

Byrnes, C. I.↗