The Partial Stability for Linear Discrete Systems

In this paper, we study the partial stability of linear discrete systems by means of Liapunov's functions of quadratic form. We obtain a necessary and sufficient condition for the system being stable with respect to part of variables and generalize Liapunov's equation to the partial stability of linear discrete systems. A method of constructing Liapunov's function of quadratic form for the stability of the systems is given.