Stability analysis of N-D discrete state–space systems

Several stability criteria for N-dimensional linear shift-invariant discrete systems described in the state–space model are presented. The criteria are the N-D state–space versions of the De Carlo et al., Anderson-Jury and Lyapunov equations with complex elements stability criteria. The criteria provide sufficient and necessary conditions for the stability analysis of N-dimensional (N-D) discrete systems. This study was carried out using the generalized Roesser state–space model for N-D discrete systems. Some stability results in this paper are derived by combining this state–space model with Lyapunov theory. Several simple sufficient conditions for easy stability checking are also presented. An example is presented to illustrate the utility of the proposed analysis.