Algebraic Necessary and Sufficient Conditions for Testing Stability of 2-D Linear Systems

The stability of two-dimensional (2-D) linear systems, continuous, discrete, and mixed (hybrid) cases with real or complex coefficients, is considered in this article using a single formalism. Algebraic necessary and sufficient conditions for testing the stability of these systems are developed. The conditions are based on the characteristic polynomial to be void of zero in the stability region which depends on the case being considered. These conditions consist of the stability test of few real univariate polynomials and a real generalized eigenvalue problem. The resulting stability test requires reduced computational complexity compared to existing techniques. A numerical example is given to illustrate the merits of the proposed approach.