Stabilization of linear boundary control systems of parabolic type: An algebraic approach (Q2712214)

The stabilization problem for a class of linear boundary control systems of parabolic type by means of feedback control is discussed. The investigated boundary control system with state \(u= u(t)\) is described by the system of equations NEWLINE\[NEWLINE{\partial u\over\partial t}+ {\mathcal L}u= 0,\quad \tau u= \sum^M_{k=1} f_k(t)\overline h_k(\xi),\quad u(0,x)= u_0(x),NEWLINE\]NEWLINE where \(f_k(t)\) denotes the control inputs and \(\overline h_k(\xi)\) actuators on the boundary, which consists in a finite number of smooth components of dimension \(m-1\). In the main theorem, the existence of such a representation for the control inputs which guarantees feedback stabilization is proved.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00050].