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Observer-based robust control for fractional-order nonlinear uncertain systems with input saturation and measurement quantization. (English) Zbl 1434.93016

Summary: The paper is concerned with the observer-based robust control problem for fractional-order (FO) nonlinear uncertain systems subject to control input saturation and measurement quantization, in which the fractional commensurate order satisfies \(\alpha \in(0, 1)\). The state measurements of observer are quantized by a logarithmic quantizer. Firstly, by introducing a continuous frequency distributed equivalent model of fractional integrator, sufficient condition for guaranteeing the asymptotic stability of closed-loop FO systems is established via the indirect Lyapunov approach. Then, by using matrix’s singular value decomposition (SVD) and linear matrix inequality (LMI) technique, the co-design problem of desired observer and controller gains are derived, which will be shown that the solution guarantees the stability of closed-loop FO nonlinear uncertain control systems. Finally, a simulation example is given to illustrate the validity of this method.

MSC:

93B35 Sensitivity (robustness)
93B53 Observers
93C15 Control/observation systems governed by ordinary differential equations
26A33 Fractional derivatives and integrals
93D20 Asymptotic stability in control theory
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information

Software:

FOTF Toolbox; FLOreS
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References:

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