The controllability of an interval linear discrete system

Controllability Robustness of Linear Interval Systems with/without State Delay and with Unstructured Parametric Uncertainties

“…If we only consider the robust controllability problem of linear interval systems with/without state delay (i.e.,̃= 0,̃= 0, and̃= 0), the sufficient condition in (16) or (26) can be, respectively, simplified as…”

“…Furthermore, it can be found that the result given by Chen and Chou [20] can be viewed as a special case of (16) and (28). On the other hand, by applying the evolutionary optimization methods [38] to choose the best matrices 0 , 0 , and 0 , the conservatism of (16), (26), (28), and (29) can be reduced.…”

“…Then, the controllability problem of continuous linear time delay systems has been studied by some researchers (see, e.g., [2,[5][6][7][8][9][10][11][12][13][14][15]). On the other hand, the problems of controlling objects whose models contain interval uncertainties arise from the control theory, differential games, operations research, and other areas of engineering and natural sciences [16]. However, the results reported in the literature [2,[5][6][7][8][9][10][11][12][13][14][15] cannot be applied to solve the robust controllability problems of the linear interval systems with state delay.…”

“…Recently, the robustness issues of interval multiple-inputmultiple-output (MIMO) systems without state delay have been studied by many researchers (see, e.g., [16,17,[21][22][23][24][25][26][27][28][29][30][31] and references therein). But, till now, only a few researchers studied the controllability issue of the interval MIMO systems without state delay [16,[19][20][21][22][23][24][25]31]. The approaches proposed by Zhirabok [24] and Ashchepkov [16,25] need to consider the solvability of dynamic systems.…”

“…But, till now, only a few researchers studied the controllability issue of the interval MIMO systems without state delay [16,[19][20][21][22][23][24][25]31]. The approaches proposed by Zhirabok [24] and Ashchepkov [16,25] need to consider the solvability of dynamic systems. Most notably, the methods proposed by Cheng and Zhang [21], Ahn et al [22], Chen et al [23] as well as Chen and Chou [19,20,31] give algebraically elegant derivations.…”