Non-synchronized H∞ estimation of discrete-time piecewise affine systems: An LMI approach

This paper designs an H_infin estimator for discrete time piecewise affine systems in the presence of external disturbance. The issue considered is that the transitions of actual system state and its estimate may not be synchronized due to output noise and estimation errors. The piecewise quadratic Lyapunov function technique is adopted, and the region information is taken into account to reduce design conservatism. Moreover, by outer approximating polyhedral regions with ellipsoids, the conditions that guarantee the estimation error systems to be globally asymptotically stable with optimized H_infin performance can be formulated as a set of linear matrix inequalities. An example is presented to verify the proposed theoretical results.