Event triggered robust filter design for discrete-time systems

This study introduces a general event triggered framework of state estimation for discrete-time systems with parameter uncertainties residing in a polytope. A robust filter is designed to ensure the ℓ₂ stability from disturbance to the estimation error and to minimise the ℓ₂ gain subject to both packet rate and size constraints. The number of data transmission and the data size are reduced by the utilisation of an event detector and a logarithmic quantiser, respectively. The event detector compares the current output measurement with the last transmitted measurement: if the difference is beyond a prescribed percentage of the current measurement, then the current measurement is transmitted to the quantiser. The quantiser encodes the measurement before sending to the filter via a digital communication channel. Conditions for filter design are found using polynomially parameter-dependent Lyapunov functions, which generalise the results using quadratic and linearly parameter-dependent Lyapunov functions. The usefulness of the techniques is demonstrated with an illustrative example.