On stability and performance analysis of discrete uncertain systems

This paper presents a new linear matrix inequality based stability result for uncertain discrete-time linear systems, which is derived by defining a multiple-Lyapunov function and by using a new bounding technique. This new bounding technique has two advantages: (1) possible to yield less conservative results, which is shown via a numerical example; and (2) flexible to cope with more complicated problems, which is illustrated by presenting a new H-infinity performance condition. It is anticipated that the idea behind this paper can be further extended to deal with synthesis problems.