Convergence and stability analysis of time-varying infinite-dimensional systems

In this paper, we investigate the stability of time-varying infinite-dimensional systems. We establish conditions for stabilization, uniform stabilization, asymptotic stabilization, and uniform practical exponential stabilization in Banach spaces using Lyapunov functions. We ensure the global convergence of solutions and outline conditions for stabilizing time-varying evolution equations in Hilbert spaces. Additionally, we provide illustrative examples to demonstrate the applicability and usefulness of the stability theory for partial differential equations.