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

A method for computing the 2-D stability margin

“…The method of the inners determinant has the same multiplexity as the method of the Schur-Cohn ( [9]), but it is actually an essential simplification of the Schur-Cohn method as far as the formulation of the various matrices is concerned [9], [12]. For this reason, the proposed method is better than that of [3]- [8].…”

“…We denote S S S, the set S S S = f(k1) with (k 1 )> 0g, where > denotes positive innerwise for all z 2 with z 2 = e j and 2 2 [0; 2] [9]. We also denote detfS S Sg the subset of the real numbers which consists of all the determinants of (k1) that belong to S S S. Evidently, detfS S Sg is the set of all the (strictly) positive real numbers.…”

“…The method is based on a constrained optimization problem of a real positive parameter. Since the formulation of the inners determinant [9] is more "direct" than the formulation of the Schour-Cohn matrix [1], [12], the method, offering a more direct computation of the stability margin, is better than the method of [3].…”

“…In this brief, a new method is proposed. It is based on a recently proposed method for checking the stability of a 2-D system via inners determinants [9].…”

Stability testing of 2-D discrete linear systems by telepolation of an immittance-type tabular test

“…(A tabular test is bound to have this order of complexity if it ends with a polynomial of degree or a symmetric polynomial of double degree). The determinant methods were based on testing determinants of various "stability" matrices (Schur-Cohn Bezuotian, Sylvester resultants, Inner matrices and more) with polynomial entries, e.g., [7] and earlier works surveyed in [4]. These determinant solutions are too of exponential complexity.…”