Derivation of new and existing discrete-time Kharitonov theorems based on discrete-time reactances [digital signal processing]

The stability of a continuous-time linear time-invariant system with an uncertain characteristic polynomial has been analyzed by Kharitonov and other researchers. An interesting proof of Khari-tonov's continuous-time stability theorem, based on reactance functions , has recently been advanced. Some of Kharitonov's results have been partially extended to discrete-time systems recently. On the other hand, the use of discrete-time reactances in digital signal processing was noticed by Schuessler over a decade ago. In this paper we first use a discrete-time reactance approach to give a second proof of existing discrete-time Kharitonov-type results. We then use the same reactance language to derive a new discrete-time Kharitonov-type theorem which, in some sense, is a very close analog to the continuous-time case. We also point out the relation between discrete-time reactances and the technique of line-spectral pairs (LSP) used in speech compression.