Switched-Gain Observers for Linear Systems by Using Max/Min Lyapunov Functions

A new switched-gain observer for linear systems subject to bounded disturbances is proposed. Specifically, we formulate the problem of constructing bimodal switched-gain observers within a hybrid systems framework, and establish novel conditions based on max/min Lyapunov functions to ensure positive invariance of the estimation error. The invariant sets are described by sublevel sets of such Lyapunov functions, which can be found by solving conditions given in terms of bilinear matrix inequalities. The observer design stems from solving such conditions by using grid search methods based on linear matrix inequalities. Numerical results are reported to show improvements with respect to previous design methods.