Robust ℋ_∞ Non-Synchronized State Estimation of Uncertain Discrete-Time Piecewise Affine Slab Systems

This paper investigates the problem of robust ℋ_∞ state estimation for a class of uncertain discrete-time piecewise affine systems where state space instead of measurable output space partitions are assumed so that the filter implementation may not be synchronized with plant state trajectory transitions. The objective is to design an admissible state estimator guaranteeing the asymptotic stability of the resulting filtering error system with a prescribed ℋ_∞ disturbance attenuation level. Based on a piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, two different approaches are developed to the robust filtering design for the underlying piecewise affine systems. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.