Unknown input nonlinear observer design for continuous and discrete time systems with input recovery scheme

摘要

In the present work, nonlinear observer design using differential mean value (DMV) theorem is extended to the design of nonlinear unknown input observer. To address the unknown input, famous approach of decoupling the unknown input has been used. Here, by the use of differential mean value theorem, the problem of designing unknown input observer evolves as stabilization of linear parameter varying system. On the basis of Lyapunov approach, linear matrix inequality (LMI) conditions for the existence of such observer are derived. For nonlinear systems, large value of Lipschitz constant may render LMI infeasible. DMV theorem may address the issue by replacing Lipschitz constants with more refined constants of lesser magnitude. DMV theorem-based approach is shown to be less conservative compared to Lipschitz constant. The proposed approach is shown to be effective for both continuous and discrete time systems. For discrete time systems, unknown input recovery scheme is also presented. Extensive simulations are shown in the end for continuous time chaotic Chen system, discrete Lorenz chaotic system and flexible joint robot link system, to highlight the efficacy of proposed strategy.