New Approach to Fast and Hyperstable State Observers for Stochastic and Complex Systems

This paper is concerned with the fast state observer for a class of continuous-time linear systems with unknown bounded parameters and sufficiently slowly time varying which satisfy the usual assumptions of conventional state observer for time-invariant plants. A less conservative approach based on hyperstability analysis is proposed to deal with the tracking error involved in Popov's inequality. Sufficient conditions that ensure the asymptotic stability of the closed-loop system are established and formulated in term of a nonlinear part which is designed with appropriate proportional and derivative gains. This observer included the derivative of the estimation error. The results obtained are satisfactory and less conservative than the Lyapunov stability analysis for the estimation error dynamic system. Also, it is showed that with a good choice of Proportional-Derivative (PD) gains, it is possible to reduce in this case to zero, the estimation error on the one hand, and on the other hand to reduce it to small residues in an asymptotic way. Finally, a numerical example of a lateral motion of CESSNA 182 aircraft system is presented to reconstruct the sideslip angle and the roll angle, respectively, and to highlight the efficiency of the approach that has been developed.