A new method to make descriptor systems regular and impulse-free by output feedback (Q2774095)

The present note is devoted to the regularizing of descriptor systems by output feedback. The descriptor systems under consideration are of the form NEWLINE\[NEWLINE\Sigma: \begin{cases} E\dot x=Ax+Bu,\;Ex(0)=x_0,\\ y=Cx, \end{cases}NEWLINE\]NEWLINE where \(x\in\mathbb{R}^n\), \(y\in\mathbb{R}^m\), \(u\in\mathbb{R}^r\), \(A,E\in\mathbb{R}^{n\times n}\), \(B \in \mathbb{R}^{n\times r}\), \(C\in\mathbb{R}^{m \times n}\), \(\text{rank} E=p<n\).NEWLINENEWLINENEWLINEA sufficient and necessary condition for regularizing the descriptor system \(\Sigma\) by output feedback was obtained by \textit{V. Lovass-Nagy}, \textit{D. L. Powers} and \textit{R. J. Schilling} [IEEE Trans. Autom. Control 39, 1507-1509 (1994; Zbl 0800.93542); ibid. 41, 1689-1690 (1996; Zbl 0875.93204)] and was formulated by means of the corresponding restricted system \(\Sigma_1\) equivalent to system \(\Sigma\).NEWLINENEWLINENEWLINEBy using the strong equivalent transformation due to \textit{G. Verghese}, \textit{B. C. Levy} and \textit{T. Kailath} [ibid. 26, 811-831 (1981; Zbl 0541.34040)], the present author transforms system \(\Sigma\) to a simpler new form and gives a new alternative version of the criterion proved by V. Lovass-Nagy et al. in the above-mentioned articles.