Discussion on: ``\((A,B)\)-invariance conditions of polyhedral domains for continuous-time systems'' by C. E. T. Dórea and J. -C. Hennet
As is clear from the title, this paper contains a discussion regarding the article of \textit{C. E. T. Dórea} and \textit{J.-C. Hennet} [Eur. J. Control 5, No. 1, 70-81 (1999; Zbl 0943.93018), see above]. Using the vertex representation of a polyhedral, the authors obtain dual equivalent conditions for this polyhedral to be \((A,B)\)-invariant. This result can be used to obtain equivalent conditions for \((A(t),B(t))\)-invariance of a polyhedral set, where \(A(t)\), \(B(t)\) are time-varying convex combination of some fixed matrices. Furthermore, the authors discuss the problems of infinite-directions, construction of the supremal \((A,B)\)-invariant set, and the feedback design. In the second section of this paper, Dórea and Hennet give their reaction on the new equivalent condition and the problems discussed in the first section.
vertex representation of a polyhedral set
scientific article; zbMATH DE number 1343404