This innovative book provides a systematic study of matrix Liapunov functions, incorporating new techniques for the qualitative analysis of nonlinear systems encountered in a wide variety of real-world situations.

Written by an expert in the area of stability analysis, Stability by Liapunov's Matrix Function Method with Applications models the stability of actual objects using ordinary differential equations, singularly perturbed systems, and high-dimensional stochastic systems tests the multistability of motion in large-scale systems using matrix-valued functions details the classic direct Liapunov method and its variants compares scalar, vector, and matrix-valued Liapunov functions proposes a new generalization of the matrix-valued auxiliary function formulates the criteria of motion stability using special matrices extends auxiliary functions to make the direct Liapunov method more powerful and more!

With over 650 equations and references, Stability by Liapunov's Matrix Function Method with Applications will appeal to pure and applied mathematicians; applied physicists; control and electrical engineers; communication network specialists; probabilists; performance analysts; applied statisticians; industrial engineers; operations researchers; and upper-level undergraduate and graduate students studying ordinary differential equations, singular perturbed equations, and stochastic equations.