On the application of matrix Lyapunov functions in motion analysis of lumped and distributed parameter systems

A. A. Martynuk

The paper develops Lyapunov’s direct method on the basis of the concept of matrix-function (don’t confuse it with a scalar function in the vector-matrix notation). The equilibrium state stability of the above-mentioned systems is investigated both by the immediate application of matrix-function and by transfer to a scalar function. It is shown that the second level decomposition yields naturally the introduction of matrix-function with a subsequent construction of stability criteria in terms of the property of having fixed sign of suitable matrices in the cone. In the paper a two-component system is also considered.