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O ver the past eight years a vast outflow of research and publications has resulted from the use of Liapunov's "second (or direct) method" of stability analysis. This work stems from the appearance of the original work of Liapunov in 1892, more than half a century ago, but only recently has this concept been appreciated to the point where workers in the area of stability of dynamic systems and automatic control are aware of its potentialities.