Sensor allocation with guaranteed exponential stability for linear multi-rate sampled-data systems

Abstract

Summary This paper addresses sensor allocation with guaranteed exponential stability for linear multi‐rate sampled‐data systems. It is assumed that a continuous‐time linear plant is exponentially stabilized by a continuous‐time linear controller. Given sensors with incommensurate sampling rates, the objective is to allocate each state to a sensor such that the resulting multi‐rate sampled‐data system remains exponentially stable. The main contributions of this paper are twofold. First, we propose sufficient Krasovskii‐based conditions to partition the state vector among sensors such that exponential stability of the closed‐loop system is guaranteed. Second, the problem of finding a partition that guarantees exponential stability is cast as a mixed integer program subject to linear matrix inequalities. The theoretical results are successfully applied to two robotic problems: path‐following in unicycles and hovering in quadrotors. Copyright © 2015 John Wiley & Sons, Ltd.

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