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.