$\mathcal{L}_2$ State Estimation with Guaranteed Convergence Speed in the Presence of Sporadic Measurements
For control engineers dealing with networked or event-triggered systems, this provides a method to ensure convergence speed despite irregular measurements.
The paper proposes an observer for linear time-invariant systems with sporadic measurements and external perturbations, achieving global exponential stability with a guaranteed decay rate and L2 robustness. The design uses linear matrix inequalities and is validated on three examples.
This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples.