Abstract
A control system designer usually prefers to use rational controllers. The question of when such a controller exists is considered in this chapter, for the class of systems composed of a delay element e −hs with interval (finite or infinite) uncertainty in h, followed by a plant characterized by a rational transfer function. Explicit conditions for the existence of such controllers, are given. Also, a computationally tractable design method, which explicitly yields the entire set of all constant gain controllers which robustly stabilize a family of systems with uncertainty, is described. A desired “optimal” controller may then be selected from the feasible set. The method is extended to the case when the rational part of the plant has uncertainties too, and is represented by a transfer function with independent interval coefficients. Illustrative numerical examples are provided.
This work was supported by grant no. 94-00010 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel, and by the Fund for the Promotion of Research at the Technion.
Research of this author is partially supported by NSF grant ECS-9418709
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Naimark, L., Kogan, J., Leizarowitz, A., Zeheb, E. (1998). On rational stabilizing controllers for interval delay systems. In: Dugard, L., Verriest, E.I. (eds) Stability and Control of Time-delay Systems. Lecture Notes in Control and Information Sciences, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027486
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DOI: https://doi.org/10.1007/BFb0027486
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