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A square matrix F is said to be D-stable if the eigenvalues of DF have negative real parts for any diagonal matrix D with positive diagonal elements. The perturbational properties of D-stability and block D-stability, a ...

Time-scale separation and stability of linear time-varying and time-invariant multiparameter singular perturbation problems are analyzed. The first problem considered in the paper is that of deriving upper bounds on the ...

A new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system. General time invariant systems with a single small parameter are considered. The paper employs ...

Local bifurcation control problems are defined and employed in the study of the local feedback stabilization problem for nonlinear systems in critical cases. Sufficient conditions are obtained for the local stabilizability ...

The stability of time-invariant multiparameter singular perturbation problems is considered and the implications of two time-scale stability results for multiple time-scale systems are clarified. An example shows that the ...

A simple proof is presented for a well known fact about Hopf bifurcation: if the loss of an equilibrium point results in periodic solutions via Hopf bifurcation, then the stability ot these periodic solutions is determined ...

Explicit upper bounds are obtained for the singular perturbation parameters of a general uniformly asymptotically stable multiparameter singularly perturbed system. The study focuses on the linear time-varying case studied ...

The asymptotic stability of a general linear time-invariant multiparameter singular perturbation problem is studied with no a priori assumptions on the relative magnitudes of the small parameters. Thus the results apply, ...