Transformations of a class of time-varying multivariable control systems to block companion forms
Transformation of time-varying multivariable systems into canonical form is presented. For a controllable canonical transformation, n must be divisible by m, the number of inputs. It is shown that the system can be transformed into canonical form if and only if \(\{A(t),B(t)\}\) is uniformly controllable with controllability index \(r=n/m\). Likewise, for an observable canonical transformation, n must be divisible by p, the number of outputs. It is shown that the system can be transformed into observable canonical form if and only if \(\{C(t),A(t)\}\) is uniformly observable with observability index \(q=n/p\). The procedure of this paper is an extension of that of the first author and \textit{Y. T. Tsay} [IEEE Trans. Autom. Contr. AC-27, 199-203 (1982; Zbl 0471.93016)].
scientific article; zbMATH DE number 4033584