Necessary and sufficient conditions for the controllability of linear interval descriptor systems
The authors consider the linear, continuous-time descriptor system \[ \begin{aligned} E\dot x(t) &= Ax(t) + Bu(t),\\ y(t) &= Cx(t),\end{aligned} \] where \(x(t)\in\mathbb R^n,\) \(u(t)\in\mathbb R^p\) and \(y(t)\in\mathbb R^q\) are the state, input and output vectors, respectively; \(E, A\in\mathbb R^{n\times n}, B\in\mathbb R^{n\times p}\) and \(C\in\mathbb R^{q\times n}\) are system matrices. Here, \(B\) and \(C\) are of full column and row rank, respectively; \(E\) may be singular (i.e. rank \(E\leq n\)). In this paper, the regularity and controllability of the descriptor system with interval drift are investigated, i.e., \(A\) is an \(n\times n\) interval matrix which represents plant uncertainties. Sufficient conditions for controllability of all the systems \((E, A + \Delta A, B)\) are derived. Necessary and sufficient conditions for regularity and controllability of the system with interval drift are established. Three numerical examples are given to illustrate the obtained results.
scientific article; zbMATH DE number 1192892