Geodesic
On the application of matrix Lyapunov functions in motion analysis of lumped and distributed parameter systems
Theoretical and applied mechanics, Tome 14 (1988) no. 1, p. 73 .

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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. 
@article{TAM_1988_14_1_a7,
     author = {A. A. Martynuk},
     title = {On the application of matrix {Lyapunov} functions in motion analysis of lumped and distributed parameter systems},
     journal = {Theoretical and applied mechanics},
     pages = {73 },
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1988_14_1_a7/}
}
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A. A. Martynuk. On the application of matrix Lyapunov functions in motion analysis of lumped and distributed parameter systems. Theoretical and applied mechanics, Tome 14 (1988) no. 1, p. 73 . http://geodesic.mathdoc.fr/item/TAM_1988_14_1_a7/