State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals

Abstract

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

Keywords

• input-to-state stability
• Lyapunov function
• Lyapunov functionals