Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to spec...

Eigenmode solutions are very important in stability analysis of dynamical systems. The set of eigenvalues of a non-self-adjoint differential operator originated from the linearization of some Cauchy problem is investigated. It is shown that the eigenvalues are purely imaginary, and that they are related to the eigenvalues of Heun’s differential equation. These two results are used to derive the...

Stability analysis of linear circuits and systems under interval parameter uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the real eigenvalues is considered. A method for computing such bounds is suggested. It consist of setting up and solving a system of n nonlinear equations, n being the ...

In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.

I outline a uniied approach to characterizing Fr echet, limiting Fr echet, and Clarke subgradients of an arbitrary function of the eigen-values of a real symmetric matrix. In particular, I compute various subdiierentials of the k'th largest eigenvalue. This paper summarizes the results and techniques presented in detail in 4]. 1 The author wishes to thank the University of Milan, and in particu...

is the jacobian matrix of F . If this matix has n distinct eigenvalues λk (real or complex), the system can be diagonalized, and the solutions can be expressed as combinations of exponentials of the form ek. Therefore, x − x∗ → 0 if all the eigenvalues have a negative real part. If one or more eigenvalues have positive real part, |x− x∗| → ∞. Therefore, • The fixed point x∗ is stable if all the...

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...