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Full-Text Articles in Engineering Science and Materials
External Direct Sum Invariant Subspace And Decomposition Of Coupled Differential-Difference Equations, Keqin Gu, Huan Phan-Van
External Direct Sum Invariant Subspace And Decomposition Of Coupled Differential-Difference Equations, Keqin Gu, Huan Phan-Van
SIUE Faculty Research, Scholarship, and Creative Activity
This article discusses the invariant subspaces that are restricted to be external direct sums. Some existence conditions are presented that facilitate finding such invariant subspaces. This problem is related to the decomposition of coupled differential-difference equations, leading to the possibility of lowering the dimensions of coupled differential-difference equations. As has been well documented, lowering the dimension of coupled differential-difference equations can drastically reduce the computational time needed in stability analysis when a complete quadratic Lyapunov-Krasovskii functional is used. Most known ad hoc methods of reducing the order are special cases of this formulation.
Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu
Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu
SIUE Faculty Research, Scholarship, and Creative Activity
This article discusses invariant subspaces of a matrix with a given partition structure. The existence of a nontrivial structured invariant subspace is equivalent to the possibility of decomposing the associated system with multiple feedback blocks such that the feedback operators are subject to a given constraint. The formulation is especially useful in the stability analysis of time-delay systems using the Lyapunov-Krasovskii functional approach where computational efficiency is essential in order to achieve accuracy for large scale systems. The set of all structured invariant subspaces are obtained (thus all possible decompositions are obtained as a result) for the coupled differential-difference equations …