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Singularly perturbed control law for linear time-invariant delay SISO systems. (English) Zbl 1305.93095
Summary: This paper considers the problem of stabilizing a single-input single-output linear time-invariant delay system, where the parameters of the system are unknown. Using norm bounds of the unknown parameters, a low-order controller and reference model are proposed. The closed-loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. We calculate bounds $$\epsilon \in (0,\epsilon ^{*})$$ as in the book of P. Kokotović et al. [Singular perturbation methods in control: analysis and design. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics (1999; Zbl 0989.93001)], such that the uniform asymptotic stability of the linear singularly perturbed delay system is guaranteed. We show how to design a control law such that the system dynamics is assigned by a Hurwitz polynomial with constant coefficients.

##### MSC:
 93C23 Control/observation systems governed by functional-differential equations 93C70 Time-scale analysis and singular perturbations in control/observation systems 93C41 Control/observation systems with incomplete information 93D15 Stabilization of systems by feedback 93D20 Asymptotic stability in control theory
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