Control of regulators for dynamical systems in Hilbert spaces (Q1811506)

The author considers controlled dynamical systems in a Hilbert space governed by equations of the form \[ \dot z= Az+ B_1u(t)+ B_2\zeta(t), \] where \(z(t)\in H\) is the state of the system at time \(t\), \(u(t)\in U\) is a control, \(\zeta(t)\in\Sigma\) is a perturbation. Here, the author defines a class of linear dynamical regulators depending on a matrix parameter and solves the problem in question under some inequality in the frequency form. He gives an application to a control problem for systems governed by difference-differential equations.