Modulating function based algebraic observer coupled with stable output predictor for LTV and sampled-data systems
CoRR(2024)
摘要
This paper proposes an algebraic observer-based modulating function approach
for linear time-variant systems and a class of nonlinear systems with discrete
measurements. The underlying idea lies in constructing an observability
transformation that infers some properties of the modulating function approach
for designing such algebraic observers. First, we investigate the algebraic
observer design for linear time-variant systems under an observable canonical
form for continuous-time measurements. Then, we provide the convergence of the
observation error in an L2-gain stability sense. Next, we develop an
exponentially stable sampled-data observer which relies on the design of the
algebraic observer and an output predictor to achieve state estimation from
available measurements and under small inter-sampling periods. Using a
trajectory-based approach, we prove the convergence of the observation error
within a convergence rate that can be adjusted through the fixed time-horizon
length of the modulating function and the upper bound of the sampling period.
Furthermore, robustness of the sampled-data algebraic observer, which yields
input-to-state stability, is inherited by the modulating kernel and the
closed-loop output predictor design. Finally, we discuss the implementation
procedure of the MF-based observer realization, demonstrate the applicability
of the algebraic observer, and illustrate its performance through two examples
given by linear time-invariant and linear time-variant systems with nonlinear
input-output injection terms.
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