Non-asymptotic and robust estimation for a class of nonlinear fractional-order systems

This paper aims to deal with the non-asymptotic and robust estimation problem for nonlinear fractional-order systems. The motivation starts with a physical system which develops into a group of system models including linear and nonlinear, commensurate and noncommensurate, integer-order and noninteger-order ones. Different from the existing modulating functions method, the proposed method breaks through the limitation of transforming the original system into the input-output differential equation, which makes the estimation for more types of systems possible. By introducing a new class of fractional order modulating functions, the state is exactly expressed by algebraic integral formulas without knowing the initial conditions of the studied system, despite the corrupting noises in the output measurement. Finally, it is illustrated in the simulation examples that the proposed estimator not only proves to be effective in the state estimation of noninteger-order systems, but also shows its advantages in that of integer-order systems compared to the high-gain observer. (C) 2022 Elsevier B.V. All rights reserved.