Unknown input reduced order observer based synchronization framework for class of nonlinear systems

In this manuscript, LMI based approach to design Reduced Order Unknown Input Observer for nonlinear continuous and discrete time systems is proposed under the framework of contraction theory. Contraction theory is an alternative approach to analyze the stability of the systems. In comparison to Lyapunov theory, it is more general as it does not require the knowledge of equilibrium point. In present work, system dynamics is split into linear, nonlinear and unknown input part. Equivalent representation for the nonlinear vector function is achieved using Differential Mean Value (DMV) theorem which makes it tractable to the framework of contraction theory and is likely to give less conservative results. Application of DMV theorem leads the error dynamical system to evolve as Linear Parameter Varying system, which is then analyzed using convexity principle. Finally, the Linear Matrix Inequality condition is derived which is to be solved for feasibility to obtain observer design matrices. Condition for the feasibility of the LMI is also analyzed. To nullify the effect of unknown input, famous approach of decoupling the unknown input is used. The approach is extended to the design of reduced order unknown input observer for discrete time systems. Reconstruction of unknown input in case of discrete time systems is also discussed. To justify the proposed theoretical results, detailed numerical simulations are presented for chaotic Chen and Lorenz systems which are members of addressed class of nonlinear systems. © 2017, Springer-Verlag GmbH Germany.