Stability and the matrix Lyapunov equation for discrete 2-dimensional systems. (English) Zbl 0588.93052
A necessary and sufficient condition is established for the existence of positive definite solutions to the 2-D Lyapunov equation using properties of strictly bounded real matrices. It is shown that in general the 2-D Lyapunov condition is only sufficient and not necessary for the stability of a 2-D discrete system. A stable 2-D system is given for which no positive definite matrices satisfying the 2-D Lyapunov equation exist.
Reviewer: T.Kaczorek
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C35 | Multivariable systems, multidimensional control systems |
| 93C55 | Discrete-time control/observation systems |
| 15A24 | Matrix equations and identities |
| 93C05 | Linear systems in control theory |
