PDEs with distributed control and delay in the loop: Transfer function poles, exponential modes and robustness of stability
The following distributed parameter system with distributed control and a delay in the feedback loop \[ \sum^i_{j= 0} a^k_j(x) p^k_j(D_x){\partial^j\over \partial t^j} w(x,t)= \sum^i_{j= 0} b^k_j(x){\partial^j\over \partial t^j} v(t)- \sum^i_{j= 0} b^k_j(x){\partial^j \over \partial t^j} (Cw)(t-\varepsilon), \] \[ x\in I_k,\quad t>0 \] is considered and a stability result is obtained which is independent of the delay for small delays. It is required that \[ \gamma(H)= \limsup_{| s|\to\infty}| H(s)|< 1 \] (taken to avoid the poles of \(H\)), where \(H\) is the transfer function of the system.
scientific article; zbMATH DE number 1282230
scientific article