Lyapunov Functional Approach to Stability Analysis of Riemann‐Liouville Fractional Neural Networks with Time‐Varying Delays

Stability analysis of fractional delayed equations and its applications on consensus of multi-agent systems

Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent system for the given different-order system is introduced by which a new stability condition is obtained that is easier to check in practice than the conditions known up to now. Then the stabilization problem of fractional-order linear systems with different fractional orders via a dynamic output feedback controller with a predetermined order is investigated, utilizing the proposed stability criterion. The linear matrix inequality based procedure of developing stabilizing output feedback control is preserved in spite of the complexity of assuming the most complete linear controller model, with direct feedthrough parameter. The proposed stability and stabilization theorems are applicable to FO-LTI systems with different fractional orders in one or both of and intervals. Eventually, some numerical examples are presented to confirm the obtained analytical results.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/asjc.1847

Stability and Stabilization of Fractional‐Order Systems with Different Derivative Orders: An LMI Approach

This paper first proposes nonlinear spline adaptive filter based on the robust Geman-McClure estimator (SAF-RGM). The proposed algorithm is obtained by minimizing the cost function relied on the Geman-McClure estimator. Since the Geman-McClure estimator can remove outliers with large amplitude from dataset, the proposed algorithm can obtain the excellent performance in the impulsive noise. Moreover, the mean and mean square behaviors of the SAF-RGM algorithm are analyzed. Simulations are conducted to confirm that the proposed SAF-RGM algorithm achieves better performance than the existing spline nonlinear adaptive filtering algorithms. Besides, simulation results validate the theoretical conclusions.

Robust Geman-McClure Based Nonlinear Spline Adaptive Filter Against Impulsive Noise

Consensus analysis of fractional-order nonlinear multi-agent systems with distributed and input delays

In this paper, the delayed state fractional order derivative (DSFOD) is introduced into the existing traditional consensus protocol aiming to improve the robustness of fractional-order multi-agent systems against communication time delay. Both of communication channels with time-delay and without time-delay cases are considered. Based on the frequency-domain analysis and algebraic graph theory, it is shown that properly choosing the intensity of DSFOD can improve the robustness of fractional-order multi-agent systems against communication delay. Finally, a simulated example with simulations is presented to confirm the correctness and effectiveness of the theoretical results.

Consensus Control of Fractional-Order Systems Based on Delayed State Fractional Order Derivative

It has been pointed out that the nonlinear spline adaptive filter (SAF) is appealing for modeling nonlinear systems with good performance and low computational burden. This paper proposes a normalized least M-estimate adaptive filtering algorithm based on infinite impulse respomse (IIR) spline adaptive filter (IIR-SAF-NLMM). By using a robust M-estimator as the cost function, the IIR-SAF-NLMM algorithm obtains robustness against non-Gaussian impulsive noise. In order to further improve the convergence rate, the set-membership framework is incorporated into the IIR-SAF-NLMM, leading to a new set-membership IIR-SAF-NLMM algorithm (IIR-SAF-SMNLMM). The proposed IIR-SAF-SMNLMM inherits the benefits of the set-membership framework and least-M estimate scheme and acquires the faster convergence rate and effective suppression of impulsive noise on the filter weight and control point adaptation. In addition, the computational burdens and convergence properties of the proposed algorithms are analyzed. Simulation results in the identification of the IIR-SAF nonlinear model show that the proposed algorithms offer the effectiveness in the absence of non-Gaussian impulsive noise and robustness in non-Gaussian impulsive noise environments.

/pdf/two-variants-of-the-iir-spline-adaptive-filter-for-combating-qx3wopevbg.pdf

Two variants of the IIR spline adaptive filter for combating impulsive noise

Digital control of a family of time-delay feedforward systems with sparse sampling

In this paper, a critically sampled nonlinear subband structure based on the Hammerstein spline adaptive filters, called Hammerstein subband spline adaptive filter (HSSAF), for the system identification problem is presented. The proposed structure is composed of a series of Hammerstein subband spline filters, each one comprising an adaptive look-up table (LUT) followed by a linear time invariant (LTI) filter. This new kind of subband structure can be utilized to identify the Hammerstein-type nonlinear systems. The subband filters update their spline control points involved in LUT and the tap-weights of the LIT in their respective adaptation loops by using the stochastic gradient decent rule, which tries to minimize the mean squared value of the estimated subband errors. In order to mitigate the interband aliasing and performance degradation introduced by the critical sampling, anti-alias filters are inserted into the subband structure, which isolate the interband aliasing components and remove them from the subband input signal and desired signal. Some simulation results demonstrate the better performance of the proposed structure in case of a high degree of nonlinearity compared to the existing scheme.

Hammerstein Subband Spline Adaptive Filter for Nonlinear System Identification

It has been reported that a novel class of nonlinear spline adaptive filter (SAF) obtains some advantages in modeling the nonlinear systems. In this paper, a nonlinear subband structure based on the spline adaptive filters, called subband spline adaptive filter (SSAF) is presented. The proposed structure is composed of a series of subband spline filters, each one comprises a linear time invariant (LTI) filter followed by an adaptive look-up table (ALUT). In addition, the computational complexity is also analyzed. Some experimental results in the context of the nonlinear system identification demonstrate the robustness of the proposed structure.

Xueliang Liu

Papers

Consensus Control of Fractional-Order Systems Based on Delayed State Fractional Order Derivative

Two variants of the IIR spline adaptive filter for combating impulsive noise

Digital control of a family of time-delay feedforward systems with sparse sampling

Hammerstein Subband Spline Adaptive Filter for Nonlinear System Identification

Nonlinear Subband Spline Adaptive Filter