Hybrid Observer-Based Asymptotic Stabilization of Non-Uniformly Observable Systems: A Case Study

We analyze a case study of output-feedback stabilization of an unobservable equilibrium. The problem involves achieving two conflicting goals: to estimate the unmeasured states, for which the system must a priori operate in an oscillatory regime, and to stabilize an equilibrium asymptotically. To overcome this quandary we propose a novel hybrid controller that generates a piecewise constant dwindling reference designed to make the system operate in an oscillatory, yet asymptotically stable, regime. The controller relies on a previously proposed switching observer, for which we provide an original analysis of exponential convergence.