Design and analysis of time-varying extended state observer

During its rapid development in the last few years, extended state observer (ESO) has been split into two typical forms: nonlinear ESO (NESO) and linear ESO (LESO). This paper proposes a novel class of time-varying ESOs (TESOs) which inherit the advantages, and meanwhile conquer the drawbacks, of both NESO and LESO. TESO is designed as a linear time-varying (LTV) form. To tune the time-varying observer gains, TESO error dynamics is first transformed into a canonical (phase-variable) form. Then time-varying PD-eigenvalues are assigned for the canonical system based on differential algebraic spectral theory (DAST). Theorems for stability and estimate error bounds of TESO are given in the presence of unknown disturbances. Comparison simulation is conducted among TESO, LESO, and NESO, which demonstrates the great effectiveness of TESO.