Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

Abstract

This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

“…Consider a class of discrete-time nonlinear Roesser-type 2D systems described as follows: [23] 𝑥 + (s, l) = F (𝑥(s, l)),…”

“…Definition 1 [23] The discrete-time Roesser-type 2D TS fuzzy system (3) is asymptotically stable if lim s→∞, l→∞ X r = 0 with the initial and boundary conditions 𝑥 h (0, l) = f (l) and 𝑥 v (s, 0) = g(s).…”

“…Lemma 1 [23] The discrete-time Roesser-type 2D TS fuzzy system (3) is asymptotically stable if there exist appropriately dimensional matrices…”

“…More recently, the problem of stability analysis of nonlinear Roesser-type 2D systems has been well investigated in Ref. [23], where a homogeneous polynomially parameterdependent Lyapunov function and several relaxed techniques have been proposed for obtaining less conservative stability criteria. Moreover, the obtained result in Ref.…”

“…Moreover, the obtained result in Ref. [23] is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Therefore, it seems that the challenge nowadays is to improve the quality of the relaxations; for instance, in terms of efficiency, i.e.…”