Stability and instability intervals of polynomially dependent systems: An matrix pencil analysis

In this paper we present a stability analysis approach for polynomially-dependent one-parameter systems. The approach, which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach, seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix-valued functions or operators. The essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. Our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem, leading to numerically efficient stability conditions. © 2017 American Automatic Control Council (AACC).

Asymptotic analysis; Computational efficiency; Stability; System stability; Asymptotic behaviors; Asymptotic properties; Computationally efficient; Critical eigenvalues; Eigenvalue perturbation; Generalized eigenvalue problems; Matrix-valued functions; Stability and instability; Eigenvalues and eigenfunctions

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