Structural controllability and observability
A system whose parameters are not fixed is said to be structurally uncontrollable (unobservable) if it is uncontrollable (unobservable) for all values of the parameters. In this paper linear time-invariant systems of the following form are considered: \(\dot x=(A_ 0+\sum^{N}_{1}\alpha_ iA_ i)x+(B_ 0+\sum^{M}_{1}\beta_ iB_ i)u\), \(y=(C_ 0+\sum^{K}_{1}\gamma_ iC_ i)x\), where \(A_ 0\), \(B_ 0\), \(C_ 0\) are the nominal system parameter matrices, \(\alpha_ i\), \(\beta_ i\), \(\gamma_ i\) are the parameter variations, \(A_ i\), \(B_ i\), \(C_ i\) are matrices of rank one modelling the structure of the variations. The main results consist in necessary and sufficient conditions for a system of the above kind to be structurally uncontrollable (unobservable). When the matrices \(A_ i\), \(B_ i\), \(C_ i\) are of rank greater than one these conditions are only sufficient to assure structural uncontrollability. The criteria are illustrated by a few examples.
scientific article; zbMATH DE number 3989177