Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

This paper is concerned with the finite-time boundedness of two dimensional (2-D) positive continuous-discrete systems in Roesser model. By constructing an appropriate co-positive type Lyapunov function, sufficient conditions of finite-time stability for the nominal 2-D positive continuous-discrete system are established. Sufficient conditions of finite-time boundedness for the addressed system with external disturbances are also proposed. The proposed results are then extended to uncertain cases, where the interval and polytopic uncertainties are considered respectively. Finally, three examples are provided to illustrate the effectiveness of the proposed results.

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example.