Hysteresis-based switching observers for linear systems using quadratic boundedness

Switched-gain observers are investigated for the purpose of estimating the state of linear systems affected by bounded noises. Under mild assumptions, hybrid observers with switching gains are proposed and provided with stability analysis based on quadratic boundedness for the estimation error. Such observers are designed by solving optimization problems aimed at minimizing upper bounds on the estimation error in such a way as to get the smallest invariant set. The effectiveness of the proposed approach is evaluated with some numerical case studies.