Uniform High-Probability ISS Tubes for Sampled-Data State Estimation

Abstract

State estimates used in sampled monitoring and automation need bounds that remain valid between measurements. We develop a finite-horizon input-to-state-stability tube and observer co-design framework for continuous-time observers driven by sampled and held outputs. The sampled-data error model separates process disturbance, sampled measurement noise, and intersample mismatch. A horizon-level disturbance-envelope event is transferred through an ISS estimate to simultaneous containment of the complete error trajectory. Quadratic dissipation inequalities yield ellipsoidal and componentwise tubes, and semidefinite co-design minimizes normalized tube width across the three channels. A structured nonlinear extension preserves known nonlinear channels. Co-design reduces the worst normalized half-width by 31% in a linear compartment benchmark and by a factor of 22.4 in a flexible-joint benchmark.