Input‐delay approach to sampled‐data control of polynomial systems based on a sum‐of‐square analysis

Abstract

In this study, the authors develop an stabilisation condition for polynomial sampled‐data control systems with respect to an external disturbance. Generally, continuous‐time and sampled state variables are mixed in polynomial sampled‐data control systems, which is the main drawback to numerically solving the stabilisation conditions of these control systems. To overcome this drawback, this study proposes novel stabilisation conditions that address the mixed‐states problem by casting the mixed states as a time‐varying uncertainty. The stabilisation conditions are derived from a newly proposed polynomial time‐dependent Lyapunov–Krasovskii functional and are represented as a sum‐of‐squares, which can be solved using existing numerical solvers. Some additional slack variables are further introduced to relax the conservativeness of the authors' proposed approach. Finally, some simulation examples are provided to demonstrate the effectiveness of their approach.