Homogeneity-Based Finite-Time Stabilization of Linear Descriptor Systems

On Homogeneous Descriptor Systems and Homogeneity-Based Finite-Time Control of Linear Descriptor Systems

“…For example, representation of systems in the descriptor form is relevant for a number of applications, e.g., electrical circuits [12]- [14], mechanical systems with phase constraints [15], [16], chemistry and biology [17]- [19], economics [20], etc. In the present paper a new definition of The material in this paper was partially presented at the 60th IEEE Conference on Decision and Control, CDC 2021 [1]. homogeneity for descriptor systems (we refer to it as d Ehomogeneity) is introduced.…”

“…The results for ∥x∥ d E (Fig.4) are shown with the use of the logarithmic scale in order to demonstrate finite-time convergence rate. The settling time estimate is T (x 0 ) ≤ 9.16 according to(25).Fig.5and Fig.6demonstrate plots of the state vector in the presence of additive disturbances d(t) = 0 1 4 sin(2t))1 4 sin(t)) 0 T (in the system under consideration, disturbances can be caused by the presence of compression of the hull, changes in the density of seawater, sea currents, etc.) and measurement band limited noise, respectively.…”