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Zbl 0543.93005
Laub, Alan J.; Arnold, W.F.
Controllability and observability criteria for multivariable linear second-order models. (English)
[J] IEEE Trans. Autom. Control 29, 163-165 (1984). ISSN 0018-9286

The paper describes criteria for the determination of controllability, stabilizability, observability or detectability of linear second-order multivariable models of the following type $$ (1)\quad M\ddot x+(D\sb s+G)\dot x+kx=Bu;\quad y=Px+Q\dot x, $$ where $x\in R\sp n$, $u\in R\sp m$ (control vector), $y\in R\sp p$ (output vector) and $M=M\sp T>0$, $D\sb s=D\sp T\!\sb s\ge 0$, $G=-G\sp T$, $k=k\sp T\ge 0$ are matrices with appropriate dimensions. The symbol $(\sp T)$ means transpose. \par The authors claim that the presented criteria are more adequate than the traditional method for determining controllability and observability of (1) which consists in transforming to the equivalent standard matrix first-order form with state variable $\left( \matrix x\\ \dot x\endmatrix \right)$ of dimension 2n. \par This claim is supported by the fact that the resulting standard controllability and observability tests do not take advantage of the particular structure of the matrices M, $D\sb s$, G, k (i.e. symmetry, definiteness and sparsity).
[J.Geromel]

MSC 2000:: *93B05 Controllability
93B07 Observability
93C35 Multivariable, multidimensional control systems
93C05 Linear control systems
93D15 Stabilization of systems by feedback

Keywords: stabilizability; detectability; second-order multivariable models

Cited in: Zbl 0578.93006

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