In this paper, a new value set based approach is presented to study the robust stability of a fractional order plant with parametric uncertainty of the interval type by using a fractional order proportional integral controller. The concept of interval uncertainty means that the parameters of the system transfer functions are uncertain parameters that each adopts a value in a real interval. Based on the zero exclusion principle, it is necessary to check whether the value set of the characteristic polynomial for the infinite frequency range [Formula: see text] includes the origin or not. To this end, in this paper, an auxiliary function is defined. The sign of this auxiliary function within a finite frequency range verifies whether the origin is included in the value set of the characteristic polynomial or not. The upper bound and the lower bound of this finite frequency range are obtained using the triangle inequality. Finally, the results of the numerical examples are provided, which confirm the effectiveness of the paper results.
This paper deals with the robust stability analysis of a class of incommensurate fractional order quasi-polynomials with a general type of interval uncertainties. The concept of the general type of interval uncertainties means that all the coefficients and orders of the fractional order quasi-polynomials have interval uncertainties. Generally, the computational complexity of specifying the robust stability of such a quasi-polynomial is shown in this paper. To this end, the robust stability is studied by Principle of Argument theorem. In fact, by presenting two theorems and three lemmas it is shown that the robust stability of a fractional order quasi-polynomial involving the general type of uncertainty can be simply investigated without needing to plot its value set by heavy computations. Examples are attested the validity of the paper results.
In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this value set may change at some switching frequencies and the repetitive calculation of these vertices at switching frequencies leads to additional calculations. In this study initially, new necessary and sufficient conditions are proposed to check the robust stability of a delayed fractional order closed loop system. Then, a novel robust stability testing function is presented based on some vertices, which are fixed for all positive frequencies. Therefore, no additional calculation is needed to obtain the outer vertices of the characteristic function value set for any pair of the switching frequencies. Also, a finite frequency range is presented to reduce the computational cost noticeably. Eventually, three numerical examples are given to verify the efficiency of the results of this paper.
This paper investigates the robust stability of fractional-order plants suffering from interval uncertainties by using fractional-order controllers. Based on the zero-exclusion principle, at first, new necessary and sufficient criteria are proposed to analyze the robust stability of the corresponding characteristic polynomial. Then, an auxiliary function is presented to investigate the robust stability criteria. The results of this paper also help to reduce additional calculations noticeably since the vertices used in the auxiliary function are fixed for all positive frequencies. Finally, three numerical examples are given to indicate the effectiveness of the paper results.
This study investigates the event-triggered resilient recursive distributed state estimation problem for discrete-time nonlinear systems over sensor networks.An event-triggered mechanism is employed to save the limited computation resource and network bandwidth while maintaining the desired performance. A resilient Extended Kalman Filter (EKF) with consensus on estimations is developed, and consensus is first achieved with respect to the prediction estimation. The accuracy of the computed estimation is then improved via two recursive equations. By adopting the structure of the EKF, the filter gains are determined in each sensor node via utilization of an upper bound for the cross-covariance, thereby resulting in a lower computational burden. The boundedness of the estimation errors is analyzed. Simulation results are reported to illustrate the effectiveness of the proposed distributed filter.
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