Comments on "Stability and absence of overflow oscillations for 2-D discrete-time systems

Robust stability of 2-D digital filters employing saturation

“…Now, this condition can be expressed as (24) Using Lemma 1, (24) becomes (25) which can be rearranged as in (26), shown at the bottom of the page. Using the well-known Schur's complement, (26) can be put in the form (9).…”

New LMI condition for the nonexistence of overflow oscillations in 2-D state-space digital filters using saturation arithmetic

“…The question of finding conditions for the global asymptotic stability of system (1) has received a considerable attention [4,8,9,[11][12][13][14]. According to [9], system (1) is globally asymptotically stable if there exists a positive definite block diagonal matrix …”

“…However, if the number of quantization steps is large or, in other words, the internal wordlength is sufficiently long, quantization effects may be neglected when studying the effects of overflow [2][3][4]. The stability properties of 2-D discrete systems described by the Roesser model [5] have been investigated extensively [4,[6][7][8][9][10][11][12][13][14][15]. The stability of 2-D systems described by the Fornasini-Marchesini second local state-space model [16] has also received a considerable attention [15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

“…The potential applications of two-dimensional (2-D) discrete systems in image data processing, seismographic data processing, thermal processes, gas absorption, water stream heating, and so forth, (Bose, 1982; Bracewell, 1995; Kazorek, 1985; Lu and Antoniou, 1992) have received considerable attention in recent years. The stability properties of 2-D discrete systems described by the Roesser model (Roesser, 1975) have been investigated extensively (Agathoklis et al, 1989; Anderson et al, 1986; Bauer and Jury, 1990; Bauer and Ralev, 1998; El-Agizi and Fahmy, 1979; Kar, 2008a, 2008b; Kar and Singh, 1997, 2000, 2001, 2005; Leclerc and Bauer, 1994; Liu and Michel, 1994; Lodge and Fahmy, 1981; Singh, 2007; Tzafestas et al, 1992; Xiao and Hill, 1996, 1999). The stability margin of 2-D discrete systems has been studied in Agathoklis (1988), Agathoklis et al (1982) and Swamy et al (1981).…”