It has been observed that for many stable feedback control systems, the introduction of arbitrarily small delays into the loop causes instability. Therefore, robustness of stablility with respect to small delays is of great importance. The authors study the robustness with respect to small delays for exponential stability of Pritchard-Salamon systems with admissible state feedback, i.e. the exponential stability of the following systems are equivalent:x(t)=S(t)x0+∫toS(t-s)BFx(s)dsu(t)=Fx(t),x0∈V,t≥0andx(t)=S(t)x0+∫toS(t-s)BFx(s-r)dsu(t)=Fx(t-r),x0∈V,t≥0and obtain a number of necessary and sufficient conditions, particularly, frequency domain characterization for robustness with respect to small delays for exponential stability.
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