A simplified stability test for 1-D discrete systems. (English) Zbl 0588.93062
This paper shows that the stability tests for 1-D discrete systems using the transformation \(p=(z+z^{-1})\) and properties of Chebyshev polynomials developed previously can be directly obtained from the z- domain continued fraction expansion based on the functions \((z+1)\) and \((z^{-1}+1)\) on an alternate basis. Furthermore, it is shown that the root distribution of a polynomial with real coefficient can be determined by the same algorithm.
MSC:
| 93D99 | Stability of control systems |
| 30B70 | Continued fractions; complex-analytic aspects |
| 93C55 | Discrete-time control/observation systems |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 93B17 | Transformations |
Keywords:
stability tests; 1-D discrete systems; Chebyshev polynomials; z-domain continued fraction expansionReferences:
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