Memory State-Feedback Control for a Linear System With Time-Varying Delay Based on the Tuning Matrix Search Algorithm

A multiple augmented Lyapunov function (MALF) is a function that includes more than one augmented matrix, allowing for a more precise evaluation of the relationships between different states within a system and facilitating the analysis of system stability. However, employing multiple augmented matrices can complicate the process of designing controllers. For this issue, this article proposes a controller synthesis algorithm to address the complexity of controller design resulting from multiple augmentation matrices. First, a memory state-feedback control criterion with tuning matrices is derived by constructing an MALF. Second, a tuning matrix search algorithm is proposed to provide appropriate tuning matrices for the memory state-feedback control criterion, leading to the determination of optimal controller gains. Finally, the effectiveness and advantage are verified by simulation of load frequency control for in the power system and H infinity$$ {H}_{\infty } $$ control for a linear singular time-delay system.