Exponential stability and controller design for linear systems with mixed interval time-varying delays

This work focuses on the exponential stability and state-feedback controller (SFC) design problems for linear systems with mixed time-varying delays (MTVDs). Initially, a sufficient condition to guarantee the exponential stability with any prescribed \(\beta -\) $\beta -$ convergence rate of the nominal unforced system under consideration is derived, utilizing the Lyapunov–Krasovskii functional (LKF) technique. Second, the problem of designing a SFC such that the closed-loop system (CLS) is \(\beta -\) $\beta -$ exponentially stable is addressed. Finally, two numerical examples and simulation results are provided to demonstrate the effectiveness of the suggested analysis and design methodologies.