Control Lyapunov Functions

Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

“…The control design based on PDE models has one technical limitation: the theory of PDEs is not supported with a well‐established common methodology for analysis and design of control systems with state‐dependent discontinuities such as to Filippov's method 37 for discontinuous ODEs and sliding mode control system 50 . Some ideas for possible expansion of the sliding mode (discontinuous) control methodology to infinite dimensional system can be found in Reference 38. However, this technique is far to be universal, well‐recognized and easy‐to‐use.…”

“…In the delay‐free case, the analysis of the closed‐loop dynamics is based on the Filippov's theory of discontinuous differential equations 37 . Its analog for PDEs with discontinuous controllers is not yet well‐developed, despite of some interesting recent contributions to this field 38 . We extend the results obtained in the delay‐free case to the input delay LTI system by means of the Artstein's transformation, 39 which allows both the stability and the robustness analysis of the closed‐loop system to be realized easily.…”