Stability of nonlinear 2D systems described by the continuous-time Roesser model

Lyapunov theory for continuous 2D systems with variable delays: Application to asymptotic and exponential stability

“…Remark 2: It is worth noting that for condition (4), the bound of the boundary conditions (ρ) is explicitly taken into account in the definition of exponential stability, contrary to the case without delay previously studied in [7].…”

“…Proof: To prove the asymptotic stability, we use similar arguments as [7]. Integrating the two components of the vector function (5) along this line, one gets…”

“…For instance, in [16], stability conditions for nonlinear time-varying discrete Fornasini-Marchesini system were proposed. In [18], [22], alternative types of stability for nonlinear discrete Roesser models were addressed, whereas [7] was dedicated to sufficient conditions of exponential stability in terms of vector function for 2D nonlinear continuous Roesser model. This paper focuses on continuous 2D systems with delays.…”

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

“…For discrete two-dimensional (2D) systems, the most popular are the structures of the state-space models proposed by Roesser [4], Fornasini and Marchesini [5,6], and Kurek [7]. These models are also adopted for continuous domain in [8][9][10][11].…”

Stability analysis of two‐dimensional switched non‐linear continuous‐time systems

“…Recently, two dimensional (2‐D) systems have drawn a lot of attention due to their broad applications in many areas such as multi‐dimensional digital filtering, linear image processing, signal processing, and process control [6–8]. Many significant results on stability of 2‐D linear systems [9–15] and 2‐D non‐linear systems [16–22] have been obtained in the literature. To name a few, several Lyapunov theorems for checking asymptotic and exponential stability of 2‐D non‐linear discrete systems based on the Roesser model were developed in [20], stability of a system described by the time‐varying non‐linear 2‐D Fornasini–Marchesini model was investigated in [21], and a sufficient condition for exponential stability of 2‐D non‐linear systems described by the continuous‐time Roesser model was established in [22].…”