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Sensor allocation with guaranteed exponential stability for linear multi-rate sampled-data systems. (English) Zbl 1334.93115

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.

MSC:

93C57 Sampled-data control/observation systems
93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
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