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A Lyapunov function of two-dimensional linear systems. (English) Zbl 0592.93051
Summary: A Lyapunov function for a two-dimensional time-invariant discrete linear system is introduced, using the two-dimensional system model given by R. P. Roesser [ibid. AC-20, 1-10 (1975; Zbl 0304.68099)]. The Lyapunov function may be used to investigate the asymptotic stability of the two-dimensional system. Previous work dealing with asymptotic stability of two-dimensional systems [see e.g. A. R. E. Ahmed, ibid. AC-25, 551-552 (1980; Zbl 0429.93051)] is based upon the location of roots of the characteristic polynomial in the closed polydisk U ¯ 2 .
MSC:
93D20Asymptotic stability of control systems
93C05Linear control systems
93C35Multivariable systems, multidimensional control systems
70G10Generalized coordinates; event, impulse-energy, configuration, state, or phase space
93C55Discrete-time control systems
93D05Lyapunov and other classical stabilities of control systems