Admissible disturbance sets for discrete perturbed systems (Q2730873)

Consider the bilinear difference equation NEWLINE\[NEWLINE x(n+1) = A x(n) + D e(n) + f(n) B x(n), \quad y(n) = C x(n), NEWLINE\]NEWLINE where \(A\), \(B\), \(C\), and \(D\) are matrices of appropriate sizes, \(x\) is the state, \(y\) is the output, and \(e, f\) denotes disturbances. These disturbances are assumed to be active only during a finite time interval. The aim of the paper is the characterize the set of \(\varepsilon\)-admissible disturbances, that are disturbances for which the unperturbed output is less than \(\varepsilon\) alway from the actual output. If \(A\) has all its eigenvalues within the unit circle, and \((A,C)\) is observable, then the set of \(\varepsilon\)-admissible disturbances is characterized. Furthermore, a numerical algorithm is provided, which is illustrated by many examples.