P. H. Bauer Department of Electrical Engineering University of Notre Dame Notre Dame, IN 46556-5637
To appear in Journal of the Franklin Institute
Abstract This paper addresses the asymptotic stability of linear time-variant polynomials whose coefficients are uncertain in an m-dimensional hyperdiamond. The approach used here allows the construction of regions in the coefficient space guaranteeing asymptotic stability that extend beyond the region specified by existing results. The necessity of the condition derived in this paper will be discussed for some special cases.
1996 IEEE International Symposium on Circuits and Systems, Vol. 2, pp. 17-20 Abstract This paper describes a sufficient condition for the stability of 1-D polynomials with shift-variant coefficients. The results presented here allow less restrictive regions in the parameter space for the choice of coefficients than do previous results.
Multidimensional Systems and Signal Processing, Vol. 7, pp. 211-220, April 1996 Abstract This paper addresses the BIBO (bounded-input bounded-output) stability of a class of discrete 2-D quarter-plane filters in the presence of nonessential singularities of the second kind (NSSK's) on the unit bidisk. Conditions under which the double bilinear transformation (DBT) preserves stability are derived. The results presented here also extend the class of systems whose stability can be predicted. Use of the inverse DBT to produce a continuous equivalent of the discrete 2-D transfer function allows easy application of a continuous-domain equivalent of a criterion developed by Dautov. The necessary and sufficient condition for stability derived in this work provides a simple check for the class of systems under consideration. From this class of systems, it is also possible to construct stable pairs of mutually inverse transfer functions.
IEEE Transactions on Circuits and Systems, Part I, Vol. 42, pp. 477-479, August 1995. Abstract This paper addresses the robust asymptotic and BIBO (bounded-input bounded-output) stability of a class of linear shift-variant multidimensional systems. Using a shift-invariant comparison system, necessary and sufficient conditions for the stability of the entire family of systems are derived.
Proceedings, 38th Midwest Symposium on Circuits and Systems, pp. 482-485, August 1995. Abstract The results described in this paper provide conditions for the asymptotic stability of 2-D shift-variant uncertain systems expressed using the Roesser state-space description. A necessary and sufficient condition for the asymptotic stability of 1-D systems involves checking all products of extreme matrices. The same test is shown to apply to 2-D systems, although the corresponding stability condition is sufficient, but not necessary.
Proceedings, 1995 IEEE International Symposium on Circuits and Systems, Vol. 2, pp. 785-788, May 1995. Abstract This paper addresses the asymptotic stability of linear shift-variant difference equations whose coefficients are uncertain in an m-dimensional hyperdiamond. The approach used here allows the construction of regions in the coefficient space guaranteeing asymptotic stability that extend beyond the region specified by existing results.
Multidimensional Systems and Signal Processing, Vol. 5, pp. 455-462, October 1994. Abstract This paper addresses the asymptotic stability of multidimensional systems represented by first hyperquadrant causal linear difference equations whose coefficients are shift-varying. The results extend previous 1-D results, and include the derivation of a fixed region of stability in the parameter space, as well as a sequence of shift-variant parameter regions. In the case of a fixed parameter region, the largest stable hyperdiamond centered at the origin will be obtained. For the shift-variant case, it will be shown that the instantaneous stable parameter region always includes this hyperdiamond.
Proceedings, 1994 IEEE International Symposium on Circuits and Systems, Vol. 5, pp. 137-140, June 1994. Abstract This paper addresses the BIBO (bounded-input bounded-output) stability of a class of discrete 2-D transfer functions in the presence of nonessential singularities of the second kind (NSSK's) on the unit bidisk. Conditions under which the double bilinear transformation (DBT) preserves stability are derived. The results presented here also extend the class of systems whose stability can be predicted.
Use of the inverse DBT to produce a continuous equivalent of the discrete 2-D transfer function allows easy application of a continuous-domain equivalent of a criterion developed by Dautov. The necessary and sufficient condition for stability derived in this work provides a simple check for the class of systems under consideration.