Stability tests for 2-D systems using the Schwarz form and the inners determinants

New stability tests for two-dimensional (2-D) (discrete/continuous) systems using the Schwarz form and the concept of inner determinants are presented. The properties of the Schwarz matrix are used for checking the stability of 2-D systems in state-space. Two innerwise matrices that have inner determinants equivalent to the principal minors of the Hermitian Schur-Cohn/Hermite matrix are introduced. The implementation of these new stability tests for discrete/continuous 2-D systems is discussed. The proposed methods offer a simplification by not requiring the positivity of many polynomials. The theoretical results are illustrated by nontrivial examples.<>