Abstract
This paper presents a new procedure for designing a fractional order unknown input observer (FOUIO) for nonlinear systems represented by a fractional-order Takagi–Sugeno (FOTS) model with unmeasurable premise variables (UPV). Most of the current research on fractional order systems considers models using measurable premise variables (MPV) and therefore cannot be utilized when premise variables are not measurable. The concept of the proposed is to model the FOTS with UPV into an uncertain FOTS model by presenting the estimated state in the model. First, the fractional-order extension of Lyapunov theory is used to investigate the convergence conditions of the FOUIO, and the linear matrix inequalities (LMIs) provide the stability condition. Secondly, performances of the proposed FOUIO are improved by the reduction of bounded external disturbances. Finally, an example is provided to clarify the proposed method. The obtained results show that a good convergence of the outputs and the state estimation errors were observed using the new proposed FOUIO.
Highlights
The interest in fractional derivatives and integral applications, as well as in theoretical and practical works, has grown immensely, see for example [1,2,3,4,5,6]
The work is dedicated to the problem of state estimation for nonlinear fractional order systems characterized by continuous time TS models, with unknown input ū(t)
A new approach is proposed for designing a fractional order Takagi–Sugeno unknown input observer for a nonlinear system described by fractional-order Takagi–Sugeno (FOTS) models with unmeasurable premise variables (UPV)
Summary
The interest in fractional derivatives and integral applications, as well as in theoretical and practical works, has grown immensely, see for example [1,2,3,4,5,6]. State variables are usually unmeasurable, but they can be measured by the introduction of sensors, with an additional cost, but the right choice is to estimate the state variables in order to avoid the effects of sensor and shareholder faults that may have appeared on the inputs or outputs of the system considered This justifies the research works on the state estimation of systems [48,49]. To implement a fuzzy observer for TS systems with unmeasurable premise variables (UPV), several methods have been evolved, comprising those which take account of analytical advances of an estimation error [50,51,52], and those which use the error description by a TS model with uncertainty or unorganized disruption [49].
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