Interval Estimation for Continuous-Time Linear Systems With Discrete Measurements

This paper investigates interval estimation for continuous-time linear time-invariant systems with discrete measurements. To obtain a reliable interval estimation, a novel interval estimation method is proposed by combining a robust observer gain design approach with an interval analysis method. Firstly, a robust observer synthesis approach is adopted to compute an observer gain to improve the accuracy of the point-wise estimation when the discrete measurements are available. In the case of aperiodic discrete-time measurements, a polytopic model with an additive norm-bounded term is proposed to characterize the uncertainties induced by the time-varying character of the inter-measurement interval times. Then, to cope with these uncertainties, a robust observer design method is introduced. Based on the obtained point-wise estimation, an interval estimation is achieved via an interval-based explicit reachability method. Compared with the existing results, the proposed method relies on non-restrictive assumptions and provides high estimation performance. Simulation results are presented to illustrate the effectiveness and superiority of the proposed method.