, On the other hand, under the same setting, characterizations for structural controllability in graphtheoretical terms has recently been provided in [47]; a sufficient condition for s-structural controllability, for structural (resp. s-structural) ISO, given in Chapters 2, 3, 4 are also reliant on this requirement, vol.3
, Under LTV setting with fixed graphs and dependent parameters, a graphical characterization for structural ISO can be obtained by combining the results in Chapter 3 (see Props. 12 and 13) and that in, vol.47
, However, the following problems remain open. (i) under LTI setting with dependent free parameters and arbitrary input, output and feedthrough matrices, a graphical characterization for structural ISO
, LTV setting with at least one dependent parameter, accounting for arbitrary input, output and feedthrough matrices and time-varying topology, purely algebraic characterizations and graph-theoretical characterizations for structural ISO
, et al operates under the assumption that the free parameters are free to take any value over the field of real (or complex) numbers. However, there exist setups where a free parameter is allowed to take only a finite set of values, i.e., over a finite field. Characterizations of structural controllability (and observability) over finite fields have been studied in, vol.78
The main difficulty seems to be the following: graphical characterization for structural ISO is reliant on an algebraic characterization, namely PBH-like test (see Prop. 1 in [22]). Since finite fields are not algebraically closed, i.e., not every polynomial with coefficients from a finite field will have a root in that field, the best of our knowledge, similar characterizations for structural ISO are not yet available ,
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