The main goal of this paper is to present a methodology to design interval observers for discrete-time linear switched systems affected by bounded, but unknown disturbances. Two design techniques are presented. The first one requires that the observation error dynamics are nonnegative while the second one relaxes this restrictive requirement by a change of coordinates. Furthermore, ideas of using H∞ formalism to compute optimal gains are proposed. Finally, illustrative examples highlight the performance of our methodology.

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This paper deals with unknown input interval observers for discrete-time linear switched systems. A new structure of interval observer is used to overcome the design difficulty of coordinate transformation often used in such context. The interval observer gains are computed by solving Linear Matrix Inequalities (LMI) derived from multiple quadratic Lyapunov functions (MQLF) under average dwell time switching signals.

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