Stability Matrices Research Articles

Stability Matrices and the Solvability of Certain Systems of Linear Inequalities†

Let A be a real n × nmatrix with non-negative non-diagonal elements aij(I ≠ j). Ais called a stability matrix if and only if all of its eigenvalues have strictly negative real parts. It is proved that A is a stability matrix if and only if the system Ax > 0, x > 0has no non-trivial solution. Further, one and only one of the systems Ax 0and Ax > 0, x > 0has a non-trivial solution

Analysis and synthesis of stability matrices

Analysis and synthesis of stability matrices

The vibration of frames

In this paper a method is presented for finding the natural frequencies and principal modes of undamped free vibration of a plane frame composed of a rectangular grid of uniform beams. A general method is presented for finding a set of assumed modes which may be used in a Rayleigh-Ritz analysis of the system. It is shown how the inertia and stability matrices for these modes may be found, and how the whole analysis may be set up in a matrix form, suitable for use with a digital computer. In the final section the method is applied to a simple frame and the results obtained are compared with the exact solution.

Transistor stabilization matrix

In the design of transistor networks where the bias circuits may involve several direct-coupled stages, it is sometimes difficult to obtain a simple indication of the effect of the various elements involved on the bias stability of the system. The stabilization matrix is proposed as an extension of the concept of the stability factor and examples are given of applications to several simple circuits. A procedure for calculating the stability matrices is suggested in Appendices.