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A general theory for matrix root-clustering in subregions of the complex plane. (English) Zbl 1069.93518
The authors discuss thoroughly the relation between various types of stability of dynamical or discrete systems and the location of the corresponding eigenvalues within half-planes, strips or circular regions. They then investigate the location of eigenvalues within more general plane regions. These regions are classified as \(\Gamma\)-type if they were derived from mapping half-planes, strips or circular regions by rational functions or as \(\Omega\)-type if they are bounded by curves which are the graphs of real polynomials in two real variables. For regions of \(\Gamma\)-type, location of the eigenvalues follows from the Schur-Cohn theorem for the unit disk. For regions of \(\Omega\)-type, the location is aided by theorems involving Kronecker products of matrices.

MSC:
93D99 Stability of control systems
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