Root counting, phase unwrapping, stability and stabilization of discrete time systems. (English) Zbl 0998.93035
Using standard and well-known arguments on the phase unwrapping (or phase net change) of discrete-time polynomials, it is shown how the number of stable (i.e. within the unit disk) roots is related to the distribution of real roots and signs of associated Chebyshev polynomials. An application to the very basic problem of constant feedback stabilization of a scalar linear discrete-time plant is described.
Reviewer: Didier Henrion (Toulouse)
MSC:
| 93D15 | Stabilization of systems by feedback |
| 26C10 | Real polynomials: location of zeros |
| 12D10 | Polynomials in real and complex fields: location of zeros (algebraic theorems) |
| 93B25 | Algebraic methods |
| 93C55 | Discrete-time control/observation systems |
Keywords:
polynomials; location of zeros; linear systems; stability; feedback stabilization; phase unwrapping; Chebyshev polynomialsReferences:
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