STABILITY TESTS FOR 2-D SYSTEMS: EXACT SOLUTIONS VIA MATRIX PENCIL 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 exactly by inspecting the generalized eigenvalues of the matrix pencil. The results consequently furnish 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.