### Fundamental theorem of proportional state feedback for descriptor systems

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The polynomial matrix equation ${X}_{l}{D}_{r}$ $+$ ${Y}_{l}{N}_{r}$ $=$ ${D}_{k}$ is solved for those ${X}_{l}$ and ${Y}_{l}$ that give proper transfer functions ${X}_{l}^{-1}{Y}_{l}$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function ${N}_{r}{D}_{r}^{-1}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by ${D}_{k}$. The subclass is navigated and extracted through a...

The matrix pencil completion problem introduced in [J. J. Loiseau, S. Mondié, I. Zaballa, and P. Zagalak: Assigning the Kronecker invariants to a matrix pencil by row or column completions. Linear Algebra Appl. 278 (1998)] is reconsidered and the latest results achieved in that field are discussed.

The problem of model matching by state feedback is reconsidered and some of the latest results are discussed.

A cascade scheme for passivity-based stabilization of a wide class of nonlinear systems is proposed in this paper. Starting from the definitions and basic concepts of passivity-based stabilization via feedback (which are applicable to minimum phase nonlinear systems expressed in their normal forms) a cascade stabilization scheme is proposed for minimum and non-minimum phase nonlinear systems where the constraint of stable zero dynamics imposed by previous stabilization approaches is abandoned. Simulation...

The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some conclusions...

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