This letter aims to investigate the robust stability of an interval fractional-order plant with an interval time delay by a general form of fractional-order controllers. Based on a simple graphical procedure, necessary and sufficient criteria are proposed to analyze the robust stability of an interval fractional-order plant. Then, the idea of “robust stability testing function” is extended to analyze the robust stability of the considered type of systems. Besides, an upper frequency bound is provided which is useful for the simulation purposes and it helps to reduce the computational cost. Finally, two examples are presented to verify the usefulness of the obtained results.

The intermittent nature of wind speed imposesa nonlinear behavior on the dynamics of the wind turbine. Consequently, relying on one linear controller tuned to a single specific operating point cannot guarantee a feasible performance in the whole operating region despite providing a fast solution. Besides, wind speed variations cause oscillations in the output power of the wind turbine. To tackle these issues, the Soft Switching Multiple Model Predictive Control (SSMMPC) technique is introduced in which the nonlinear dynamical model of the wind turbine is approximated by defining multiple linear models around various operating points. The gap metric is used as a mathematical tool to construct a bank of multiple linear models that results in a bank of linear controllers. By assuming a relatively small gap threshold value between the neighboring linear models, the soft switching is guaranteed. In this way, there will be no unexpected impulsive behavior in the control input during switching from one MPC to another. The closed loop system stability is studied using Lyapunov theory and a novel switching stability proof based on probabilities is provided. The SSMMPC performance is investigated and compared with a TSR-based controller and a bidirectional control method through simulations using the NREL 10 kW wind turbine model and experimental results on a 7.5 kW wind turbine drivetrain. The results corroborate the improvements that can be attained by using SSMMPC in terms of more captured energy, better maximum power point tracking quality, lower generator torque oscillations, and smoother output power curve.

This paper addresses the issue of a road-type-adaptive control strategy aimed at enhancing suspension performance. $H_2$ synthesis is employed for modeling road irregularities as impulses or white noise, minimizing the root mean square (RMS) of performance outputs for these specific road types. It should be noted, however, that this approach may lead to suboptimal performance when applied to other road profiles. In contrast, the $H_{\infty }$ controller is employed to minimize the RMS of performance outputs under worst-case road irregularities, taking a conservative stance that ensures robustness across all road profiles. To leverage the advantages of both controllers and achieve overall improved suspension performance, automatic switching between these controllers is recommended based on the identified road type. To implement this adaptive switching mechanism, manual switching is performed, gathering input–output data from the controllers. These data are subsequently employed for training an Adaptive Neuro-Fuzzy Inference System (ANFIS) network. This elegant approach contributes significantly to the optimization of suspension performance. The simulation results employing this novel ANFIS-based controller demonstrate substantial performance enhancements compared to both the $H_2$ and $H_{\infty }$ controllers. Notably, the ANFIS-based controller exhibits a remarkable 62% improvement in vehicle body comfort and a significant 57% enhancement in ride safety compared to passive suspension, highlighting its potential for superior suspension performance across diverse road conditions.

We provide a comprehensive impossibility result towards achieving string stability, i.e. keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend existing results, from the LTI setting to any homogeneous controllers that can be nonlinear, time-varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the L2-type standard and a BIBO type criterion. All results hold for a general discrete-time controller which should cover most applications.

In this paper, a distributed controller is designed for the consensus of multi‐agent systems in which each agent has a general second‐order linear dynamic and the information is exchanged over a data‐delaying communication network. Using the sensitivity of system poles to the parameters of the control protocol, graphical delay‐dependent synthesis conditions are derived to tune the controller gains. A systematic procedure is developed to attain maximum tolerable transmission delay in the system. Moreover, simpler condition is provided for the special case where the second‐order model is reduced to a double integrator. Simulation results are presented to illustrate the merits of the proposed scheme compared to some recent rival ones in the literature.