Coprime-inner/outer factorization of SISO time-delay systems and FIR structure of their optimal \(H_\infty\) controllers. (English) Zbl 1273.93063
Summary: The approach in C. Foias, H. Özbay, and A. Tannenbaum [”Robust control of infinite dimensional systems. Frequency domain methods”, Springer, Berlin (1996; Zbl 0839.93003)] is one of the well-developed methods to design \(H_\infty\) controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime-inner/outer factorization. We give the largest class of Single-Input–Single-Output (SISO) time-delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal \(H_\infty\) performance and eliminate unstable pole-zero cancellations in the optimal \(H_\infty\) controller. We extend the results on the finite impulse response structure of optimal \(H_\infty\) controllers by showing that this structure appears not only for plants with input/output delays, but also for general SISO time-delay plants.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C73 | Perturbations in control/observation systems |
| 93C35 | Multivariable systems, multidimensional control systems |
| 93C05 | Linear systems in control theory |
Keywords:
optimal \(H_\infty\) controllers; coprime-inner-outer factorization; weighted mixed sensitivity problem; finite impulse response (FIR)Citations:
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