Abstract
The module theoretic framework in linear time invariant system theory is extended to include stability considerations as well. The resulting setup is then applied to an investigation of nonsingular, causal, and stable precompensation. The main issues are resolved through the introduction of two sets of integer invariants-thestability indices and thepole indices. The stability indices characterize the dynamical properties of all the stable systems that can be obtained from a specified system through the application of nonsingular, causal, and stable precompensation. The pole indices characterize the dynamical properties of all the nonsingular, causal, and stable precompensators that stabilize a specified system.
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This research was done while the author was with the Center for Mathematical System Theory, University of Florida, Gainesville, Florida 32611, USA, and was supported in part by US Army Research Grant DAAG29-80-C0050 and US Air Force Grant AFOSR76-3034D.
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Hammer, J. Stability and nonsingular stable precompensation: An algebraic approach. Math. Systems Theory 16, 265–296 (1983). https://doi.org/10.1007/BF01744583
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DOI: https://doi.org/10.1007/BF01744583