State and input simultaneous estimation for discrete‐time switched singular delay systems with missing measurements

Abstract

SummaryThis paper presents an approach to simultaneously estimating the states and inputs of discrete‐time linear switched singular state‐delayed systems with unknown inputs, multiple missing measurements, and average dwell time (ADT) switching. In each output measurement channel of the system, the data loss incident is controlled by an individual stochastic variable obeying a certain probability distribution on the interval [01]. The proposed approach is based on the design of a switched, loss‐probability‐dependent proportional integral observer under the ℓ2 input attenuation framework. By using piecewise Lyapunov function technique, ADT scheme, stochastic analysis, and projection lemma, sufficient conditions for the existence of such an observer are established in terms of linear matrix inequalities, which guarantee that the resulting estimation error system is stochastically exponentially admissible and achieves an (non‐weighted) ℓ2 gain from the augmented unknown input to the state and unknown input estimation errors under ADT switching. Moreover, a method is provided to seek the minimum allowable ℓ2 gain level for a desired ADT of the switching signals. The effectiveness of the proposed approach is illustrated by a simulation example of direct current (DC) servomechanism control system. Copyright © 2016 John Wiley & Sons, Ltd.