Finite-dimensional representation of delay systems
The author considers the state delayed system \[ \dot x(t)= A_0 x(t)+ A_1 x(t-\tau)+ B_0 u(t),\quad x_0= \varphi,\tag{1} \] where \(\varphi\in C([-r, 0]; \mathbb{R}^n)\), \(A_0, A_1\in \mathbb{R}^{n\times n}\), \(B_0\in \mathbb{R}^{n\times m}\), \(u(t)\in \mathbb{R}^m\), \(x(t)\in \mathbb{R}^n\). It is shown that one can construct a finite-dimensional system whose partial state replicates the response of the delay system (1) up to small solutions of the homogeneous delayed system.
scientific article; zbMATH DE number 1781914
scientific article