Spatial Linear Matrix Inequalities Research Articles

Fuzzy Boundary Control for Nonlinear Delayed DPSs Under Boundary Measurements.

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Output synchronization of reaction–diffusion neural networks under random packet losses via event-triggered sampled–data control

For space-varying reaction–diffusion neural networks (RDNNs), this article mainly studies the output synchronization via an event-triggered sampled-data (ETSD) control under spatially point measurements (SPMs) with random packet losses. To reduce the communication burden, an ETSD control scheme is adopted to decrease the unnecessary SD and the update frequency of the controller. Meanwhile, the problem of random packet losses in the communication channels from controller to actuator is considered. Some synchronization criteria based on spatial linear matrix inequalities (SLMIs) are established through an ETSD controller under SPMs with random packet losses to guarantee the mean square exponential stability of synchronization error system with drive and response dynamics via utilizing inequality techniques and Lyapunov functional. Furthermore, we express SLMIs as LMIs for solving the ETSD control design problem for output synchronization of space-varying RDNNs. Finally, the effectiveness of the proposed method is demonstrated by one numerical example.

Fuzzy Control Under Spatially Local Averaged Measurements for Nonlinear Distributed Parameter Systems With Time-Varying Delay

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.