Robust controllability of linear time-invariant interval systems

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

“…Two numerical examples have been given to illustrate the applications of the proposed sufficient algebraic criteria. It has also been shown that the proposed sufficient criterion for linear interval systems having no state delay and no unstructured parametric uncertainties can obtain less conservative results than the existing sufficient criteria given by Cheng and Zhang [21], Ahn et al [22], Chen et al [23], and Chen and Chou [19,20,31].…”

“…Then, from the results obtained above in (36a), (36b), (36c), (36d), (36e), (36f), (36g), (36h), (36i), (36j), (36k), (36l), (36m), (36n), (36o), and (36p), we can conclude that the linear interval system in (30) is robustly controllable. From this example, it is clear that our proposed approach gives less conservative results than the existing methods of Cheng and Zhang [21], Ahn et al [22], Chen et al [23], and Chen and Chou [19,20,31].…”

“…That is, the interval matrices in (30) do not satisfy the assumption that all the elements in the interval matrices must have the same variations. So, the result of Chen and Chou [19,20,31] cannot be used in this example. Now, applying the sufficient criterion in the proposed condition of (29) with 2-norm-based matrix measure for the robust controllability, we have rank( 0 ) = 9, and we get…”

“…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.…”

“…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. However, the interval matrices considered by Cheng and Zhang [21] must satisfy the sign-invariant condition, and all the interval matrices considered by Chen and Chou [31] must have the same variations.…”