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