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In this technical note 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. [ABSTRACT FROM AUTHOR]

We study stabilization problems for time-varying linear systems with constant input delays. Our reduction method ensures input-to-state stability with respect to additive uncertainties, under arbitrarily long delays. It applies to rapidly time-varying systems, and gives a lower bound on the admissible rapidness parameters. We also cover slowly time-varying systems, including upper bounds on the allowable slowness parameters. We illustrate our work using a pendulum model. [ABSTRACT FROM AUTHOR]

We address the problem of stabilizing systems belonging to a family of time-varying nonlinear systems with distributed input delay through state feedbacks without retarded term. The approach we adopt is based on a new technique that is inspired by the reduction model technique. The control laws we obtain are nonlinear and time-varying. They globally uniformly exponentially stabilize the origin of the considered system. We illustrate the construction with a networked control system. [ABSTRACT FROM AUTHOR]