This article develops a novel synthesis approach for the synchronization of a network of singularly perturbed systems (SPSs) with a small singular perturbation parameter $\varepsilon$ via distributed impulsive control. First, a decoupling method in the setting of directed networks is employed to decompose networked SPSs related to complex eigenvalues of the Laplacian matrix. Then, based on an improved piecewise continuous Lyapunov function, an $\varepsilon$ -dependent synchronization criterion is established. The relationship among the impulse interval, the impulse gain matrix, and $\varepsilon$ is revealed. By employing the newly obtained synchronization criterion, some sufficient conditions on the existence of an $\varepsilon$ -dependent impulse gain matrix are derived. Finally, an example is simulated to verify the effectiveness of the theoretical results.

This paper is mainly concerned with the asynchronous control problem of fuzzy singularly perturbed systems (FSPSs) by designing an effective dynamic event-triggered control (ETC) strategy. Different from the existing results, a sample-based dynamic eventtriggering condition related to the singular perturbation parameter (SPP) " is proposed. Particularly, an auxiliary variable is employed in the eventtriggered mechanism (ETM), which changes with the fluctuation of the system state. By constructing a novel parameter-dependent Lyapunov functional, some sufficient conditions are derived to stabilize FSPSs and solve the "-dependent control gain. Furthermore, the upper bound of SPP _" related with the proposed control gain is determined. The Zeno behavior can be naturally avoided by applying the sample-based dynamic ETC. Finally, two examples including a nonlinear circuit are presented to validate the effectiveness of obtained results.

This article considers the finite-time prescribed performance control (PPC) problem for a class of nonlinear systems with mismatched disturbances in the presence of output constraints. By integrating a nonrecursive design framework into the PPC process, the proposed nonsmooth methodology alleviates the “explosion of terms” that often occurs in recursive PPC. In addition, aiming to enhance the dynamic performance of a constrained nonlinear system, a novel finite-time performance function is proposed. The final convergence time of tracking error can be predefined, independent of system initial condition and control parameters. Finally, a numerical simulation and a representative position regulation experiment of permanent magnet synchronous motor (PMSM) system validate the effectiveness and simplicity of the proposed nonsmooth control scheme.

To improve the dynamic performance and disturbance rejection capability of the permanent magnet synchronous motor (PMSM) system, an adaptive super-twisting nonsingular terminal sliding mode control (AST-NTSMC) approach based on the disturbance compensation technique is investigated in this paper. Firstly, the dynamic model of PMSM system under non-cascade structure is formulated, and two high-order sliding mode observers (HOSMOs) are designed to estimate and compensate for both matched and mismatched disturbances within the system. A composite non-cascade speed controller is subsequently developed. While a larger switching gain coefficient can enhance dynamic performance and disturbance rejection ability, it often tends to increase chattering issues. To tackle this challenge, an adaptive mechanism is proposed for the PMSM speed regulation system, allowing dynamic adjustment of the gain coefficient during the sliding mode reaching phase, which significantly enhances both dynamic and steady-state performance compared to the conventional NTSMC method. Experimental results validate the effectiveness of the proposed control approach.

This paper studies synchronization of singularity-perturbed complex networks (SPCNs) with a small singular perturbation parameter (SPP) via event-triggered impulsive control (ETIC). A novel dynamic event-triggered mechanism is proposed where an auxiliary impulse parameter is introduced to regulate the triggering threshold dynamically for saving the network resource. Based on SPP-dependent Lyapunov function, some sufficient conditions involving the impulsive gain, triggering parameters and singular perturbation parameter (SPP) are obtained to synchronize the SPCNs, and the upper bound of SPP is also determined. Moreover, it proves that the Zeno behavior can be excluded. Finally, two simulations are provided to demonstrate the validity of the obtained results.