Stability of the SDDRE based Observer for Deterministic Nonlinear Systems

Exponentially Bounded-Input-Bounded-State and Bounded-Input-Bounded-Output (BIBO) stability of the State Dependent Differential Riccati Equation (SDDRE) based observer of deterministic nonlinear time-varying systems is proved by three approaches. Each proof highlights different aspect of the SDDRE based estimator-observer stability. The proofs use the State Dependent Coefficient (SDC) form representation of nonlinear system. One approach uses results from theory of linear time-varying systems. The second approach defines Lyapunov function and uses LaSalle's invariance principle and the new invariance principle to show that the state of the SDDRE based estimator is BIBO stable. The third approach proves that the state transition matrix of the estimator is exponentially stable under specific conditions and computes bounds on the state. It is shown that uniform complete observability and controllability along the system's trajectories are sufficient for asymptotic stability.