2019/01/07 by Qian Feng, Feng, Qian, Wilfrid Perruquetti +3
Computer Science · Engineering · #Control and Stability of Dynamical Systems #Elasticity and Wave Propagation #FOS: Electrical engineering #Neural Networks Stability and Synchronization #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1901.01956
openalex publication_date 2019/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
New methods are developed for the stabilization of a linear system with\ngeneral time-varying distributed delays existing at the system's states, inputs\nand outputs. In contrast to most existing literature where the function of\ntime-varying delay is continuous and bounded, we assume it to be bounded and\nmeasurable. Furthermore, the distributed delay kernels can be any\nsquare-integrable function over a bounded interval, where the kernels are\nhandled directly by using a decomposition scenario without using\napproximations. By constructing a Krasovski ui functional via the application\nof a novel integral inequality, sufficient conditions for the existence of a\ndissipative state feedback controller are derived in terms of matrix\ninequalities without utilizing the existing reciprocally convex combination\nlemmas. The proposed synthesis (stability) conditions, which take dissipativity\ninto account, can be either solved directly by a standard numerical solver of\nsemidefinite programming if they are convex, or reshaped into linear matrix\ninequalities, or solved via a proposed iterative algorithm. To the best of our\nknowledge, no existing methods can handle the synthesis problem investigated in\nthis paper. Finally, numerical examples are presented to demonstrate the\neffectiveness of the proposed methodologies.\n