Stability of 2-D periodically shift variant filters

Finite‐region stability and finite‐region boundedness for 2D Roesser models

“…It is worth noting that in Theorem 3.1, c 2 < .1 Á/c is an implicit condition and can be derived via inequality (7). In fact, according to inequality (7), we have…”

“…In recent decades, discrete two‐dimensional (2D) models have been widely applied in iterative learning, image processing, satellite cloud picture analysis, seismological and geographical data processing, X‐ray image enhancement, and other fields . Lyapunov asymptotic stability (LAS) theory is commonly considered to be a fundamental and an important aspect of 2D models; after decades of development, research on the topic has become quite sophisticated and received several notable achievements. For example, stability analysis problems for 2D systems have been successfully investigated in as well as stabilization and H ∞ control problems for 2D systems with Markovian jump parameters .…”

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

“…Stability analysis and stabilization are the main issues in the design of any control system. Stability issues of 2-D systems have been considered by many researchers [8][9][10][11][12][13][14][15][16][17][18]. With the introduction of state-space models of 2-D discrete systems, various Lyapunov equations have emerged as powerful tools for the stability analysis and stabilization of 2-D discrete systems.…”

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

“…[1][2][3][4][5][6][7][8], the two-dimensional (2-D) systems have received considerable attention. The stability analysis of 2-D discrete systems described the Fornasini-Marchesini (FM) first model [9] have been investigated extensively [10][11][12][13][14][15][16][17][18][19][20]. In [10][11][12]20], the method of nonnegative matrix theory has been proposed for the investigation of stability of 2-D systems described by the FM first model.…”

“…Based on this connection, a novel sufficient condition for the asymptotic stability of the FM first model is obtained and it is shown by numerical simulations that the condition given in [15] is usually less conservative than that of [14]. In [16], the stability of 2-D periodically shift variant system represented by the FM first model has been studied. In [19], based on the sum-of-squares polynomials with matrix coefficients, an LMI based sufficient condition for asymptotic stability of 2-D systems described by the FM first model has been derived.…”