Strictly bounded realness and stability testing of 2-D recursive digital filters

An algorithm is presented for stability testing of 2-D recursive digital filters. The algorithm is based on the Schur-Cohn test for zero locations of 1-D complex coefficient polynomials. The authors´ derivation for 2-D stability testing is algebraic in nature. It is shown that the stability testing of 2-D recursive digital filters is equivalent to strictly bounded realness of a certain 1-D rational matrix. Furthermore, it is known that a given 1-D rational matrix is strictly bounded real if and only if there exists a minimal realization such that its system matrix is a strict contraction. The realization can be obtained by solving an algebraic Riccati equation if the system is strictly bounded real. Hence, the stability of 2-D recursive digital filters amounts to the solvability of a certain algebraic Riccati equation