We derive the solvability conditions and a formula of general solution to Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate necessary sufficient for quaternion equation, which involves ?-Hermicity. also provide algorithm with numerical example illustrate main results this paper.

Abstract We consider the problem of stabilizing PDE–ODE cascade systems in which input is applied to PDE system whose output drives ODE system. also dual constructing an observer for ODE–PDE system, measured. The these problems exponentially stable and unstable. While models plant both problems, actuator stabilization sensor problem. In literature, have been solved specific using backstepping a...

In this paper the output regulation of a linear distributed parameter system with a nonautonomous periodic exosystem is considered. It is shown that the solvability of the output regulation problem can be characterized by the solvability of a certain constrained infinite-dimensional Sylvester differential equation. Conditions are given for the existence of feedforward and feedback controllers s...