Delay/Disturbance-Tolerant Finite-Time Stabilization for Linear Systems: Inverse-Optimal Implicit-Lyapunov-Function Approach

For a class of input-delayed disturbed linear systems, this paper considers the problem of finite-time implicit-Lyapunov-function (ILF)-based control. With ILF as the evaluation of system performance, the established ILF optimality theorem reveals that the ILF-based controller minimizes a specific ILF-based meaningful cost index and provides finite-time stability. The inverse optimal idea facilitates the construction of ILF expression and exhibits two kinds of tuning weight parameters for design. Furthermore, to maintain the robustness to the input delay and disturbances, we have a tolerance set defined, according to which the controller is executed in a piecewise form. The theoretical findings are validated by numerical simulations.