Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The guarantees existence of an observer, whose gain is determined only by unstable modes system. allows observer design with low computational complexity compared to classical estimation approaches. An extension this class nonlinear proposed, and local convergence corresponding error dynamics proven. Numerical results show efficacy proposed technique.