Controllability robustness of linear interval systems with delay in control and unstructured uncertainties

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

“…For the time delay systems, there are two cases considered in the literature: (i) delay in state and (ii) delay in control input. The authors of this paper have studied the controllability problem of the uncertain/interval system with delay in control input [17][18][19], whereas the controllability problem of the interval system with delay in state is considered in this paper. Here it should be noticed that the controllability problem of the continuous linear systems with both parametric uncertainties and delay in state has been considered by Chen and Chou [20].…”

“…Here it should be noticed that the controllability problem of the continuous linear systems with both parametric uncertainties and delay in state has been considered by Chen and Chou [20]. The same mathematical means as that used by Chen et al [17,18] and Chen and Chou [19] is used in this paper, but the rationale, formulation, and concept of analyzing controllability for the delay in state case are very different from those for the delay in control input case. On the other hand, here it should be also noticed that, in the works of Chen et al [18] and Chen and Chou [19], all the elements in the interval system matrix and in the interval input matrices, respectively, are assumed to vary with both synchronous direction and same magnitude.…”

“…The same mathematical means as that used by Chen et al [17,18] and Chen and Chou [19] is used in this paper, but the rationale, formulation, and concept of analyzing controllability for the delay in state case are very different from those for the delay in control input case. On the other hand, here it should be also noticed that, in the works of Chen et al [18] and Chen and Chou [19], all the elements in the interval system matrix and in the interval input matrices, respectively, are assumed to vary with both synchronous direction and same magnitude. So, the results of Chen et al [18] and Chen and Chou [19] cannot be used to cover all matrices in the interval system.…”

“…On the other hand, here it should be also noticed that, in the works of Chen et al [18] and Chen and Chou [19], all the elements in the interval system matrix and in the interval input matrices, respectively, are assumed to vary with both synchronous direction and same magnitude. So, the results of Chen et al [18] and Chen and Chou [19] cannot be used to cover all matrices in the interval system.…”

“…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.…”