Stable Approximation of Discrete Interval Systems

Model Order Diminution of Discrete Interval Systems Using Kharitonov Polynomials

“…Similarly, second order interval models, attained by considering models given in (36), (43), (50) and (57), and (37), (44), (51) and (58) are provided in (60) and (61), respectively. [9] 0.1512 0.4737 0.7667 0.3319 Direct series and dominant pole [2] 0.0265 1.1218 0.8121 0.1959 Gamma delta approximation [19] 0.0099 0.4341 0.6167 0.1951 Direct Truncation [32] 0.0136 2.2541 0.4346 0.0381 Routh approximation [33] 0.0037 1.7388 0.6619 0.0428 Padé and dominant pole [17] 0.0348 1.0002 0.7109 0.1959…”

“…A comparative study of step, impulse and Bode responses of HOS and LOM are presented for proposed model as depicted in (62) and proposed model as provided in (63), along with the models obtained by existing methods [2], [9], [17], [19], [32], [33] The Table 6 and Table 7 provide the information and FIGURE 5. Impulse response of the original system and LOM for higher limit.…”

“…Impulse response of the original system and LOM for higher limit. [2] 0.0353 1.6920 1.6108 0.1988 Gamma delta approximation [19] 0.0217 0.8280 0.6223 0.1709 Direct Truncation [32] 0.0166 2.1404 0.4390 0.0382 Routh approximation [33] 0.0305 0.9821 0.7773 0.1831 Padé and dominant pole [17] 0.0382 0.7969 1.4126 0.3977 Direct truncation [32] Padé and dominant pole [17] Routh approximation [33] Stable approximation [9] Direct series and dominant pole [2] Bode response with lower bound Frequency (rad/s) FIGURE 6. Bode response of the original system and LOM for lower limit.…”

“…The MOD techniques are employed for diminution of large-scale systems in frequency-domain as well as in time-domain, both. Some of the predominant techniques are Padé approximation method [11], biased factor division method [12], Routh approximation (RA) method [13]- [15], stable approximation method [9], direct series and dominant pole method [2], [3], stability equation method [16], etc. Further, some other order diminution techniques utilized are mixed methods [4]- [9].…”

“…Some of the predominant techniques are Padé approximation method [11], biased factor division method [12], Routh approximation (RA) method [13]- [15], stable approximation method [9], direct series and dominant pole method [2], [3], stability equation method [16], etc. Further, some other order diminution techniques utilized are mixed methods [4]- [9]. In mixed approaches, two order diminution methods are combined in order to achieve better stable LOM.…”