Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differ...Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.展开更多
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...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.展开更多
基金Project (No. 10271111) supported partially by the National Natural Science Foundation of China
文摘Many papers on a wide range of control problems for Pritchard-Salamon systems have appeared and many of its important mathematical and system theoretical properties have been revealed. This paper deals with the differentiability of the Pritchard-Salamon system with admissible state-feedback. Spectrum analysis showed that under definite condition, the unbounded perturbation semigroup of the Pritchard-Salamon system is eventually differentiable.
文摘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.
