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Kubo, T.

Exponential stability assignment of neutral delay-differential systems by a class of linear-quadratic regulators. (English) Zbl 1061.93083

Int. J. Syst. Sci. 35, No. 3, 159-166 (2004).
The following neutral differential system \[ \dot{x}(t)=A_0x(t)+A_1x(t-h)+A_{-1}\dot{x}(t-h)+Bu(t),\tag{1} \] with a feedback control \[ u(t)=-B^{T}P(x(t)-x(t-h)),\tag{2} \] where \(P\) is an unknown matrix, is considered. Sufficient conditions for asymptotical (exponential) stability in the form of a linear matrix inequality are obtained for the closed-loop system (1), (2). It is shown that the feedback law (2) belongs to a class of optimal linear-quadratic regulators.
Reviewer: Tamaz Tadumadze (Tbilisi)

MSC:

93D15 Stabilization of systems by feedback
34K40 Neutral functional-differential equations
93C23 Control/observation systems governed by functional-differential equations
49N10 Linear-quadratic optimal control problems

Keywords:

neutral equations; asymptotic stability; delay; linear matrix inequality; linear-quadratic regulators
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