Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation

In this article, we address the delay-dependent robust stability of uncertain fractional order neutral-type (FONT) systems with distributed delays, nonlinear perturbations, and input saturation. With the aid of the Lyapunov–Krasovskii functional, criteria on asymptotic robust stability of FONT, expressed in terms of linear matrix inequalities, are constructed to compute the state-feedback controller gains. The controller gains are determined subject to maximizing the domain of attraction via the cone complementarity linearization algorithm. The theoretical results are validated using numerical simulations.

Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties

This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.

Unified Approach for Robust Stability Analysis of Buck Converters with Discrete-Time Sliding Mode Control

This paper proposes a novel discrete-time sliding mode (DTSM) control approach to address the robust stability problem of buck converters with multiple disturbances. The contributions lie in the “unified” modelling and controller design. In modelling, all the possible model uncertainties and external disturbances are considered and further classified into two cases. It can also be extended to the situations with individual/several disturbances. While for the controller design, differing from the traditional DTSM based on the nominal model, the disturbances are directly introduced in the process, giving the robust stability condition and four new regulation subranges. It is suitable for both nominal and perturbed systems. Finally, the influences of the sampling time and disturbances on the control performance are investigated. Simulations and experiments confirm the benefits of the unified approach with greater accuracy and wider applications.

Torque Ripple Suppression of PMSM Based on Robust Two Degrees-of-Freedom Resonant Controller

This paper concentrates on a robust resonant control strategy of a permanent magnet synchronous motor (PMSM) for electric drivers with model uncertainties and external disturbances to improve the control performance of the current loop. Firstly, to reduce the torque ripple of PMSM, the resonant controller with fractional order (FO) calculus is introduced. Then, a robust two degrees-of-freedom (Robust-TDOF) control strategy was designed based on the modified resonant controller. Finally, by combining the two control methods, this study proposes an enhanced Robust-TDOF regulation method, named as the robust two degrees-of-freedom resonant controller (Robust-TDOFR), to guarantee the robustness of model uncertainty and to further improve the performance with minimized periodic torque ripples. Meanwhile, a tuning method was constructed followed by stability and robust stability analysis. Furthermore, the proposed Robust-TDOFR control method was applied in the current loop of a PMSM to suppress the periodic current harmonics caused by non-ideal factors of inverter and current measurement errors. Finally, simulations and experiments were performed to validate our control strategy. The simulation and experimental results showed that the THDs (total harmonic distortion) of phase current decreased to a level of 0.69% and 5.79% in the two testing environments.