Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions

This paper studies the stability of 2-D dynamic systems. We consider systems characterized by 2-D polynomials and 2-D state–space descriptions. For each description, we derive necessary and sufficient stability conditions, which all require only the computation of a constant matrix pencil. The stability of the underlying system can then be determined by inspecting the generalized eigenvalues of the matrix pencil. The results consequently yield 2-D stability tests that can be checked both efficiently and with high precision. Additionally, frequency-sweeping tests are also obtained which complement the matrix-pencil tests and are likely to be more advantageous analytically.