State feedback and output feedback control of a class of nonlinear systems with delayed measurements (Q885336)

The paper deals with quasilinear systems. It is assumed that the output vectors \(y(t)=Cx(t)\), where \(C\) is a constant matrix and \(x(t)\) is the phase vector of the system, are measured. Two problems are discussed. The first one consists in designing a delayed state feedback controller of the form \(u(t) = Kx(t-\tau(t))\) to stabilize the given system. The second problem consists in designing of an output feedback controller such that the closed-loop system is stable. An important feature of this controller is its dependence on delayed measurements. On the basis of the Lyapunov-Krasovskii approach, the authors derive sufficient conditions for the existence of a state feedback controller and an output feedback controller in terms of linear matrix inequalities. The authors also present methods of calculating the controller gain matrices and illustrate the effectiveness of the proposed methods with numerical examples.