Input‐delay approach to sampled‐data H∞ control of polynomial systems based on a sum‐of‐square analysis. Issue 9 (1st June 2017)

• Record Type: Journal Article
• Authors: Kim, Han Sol; Park, Jin Bae; Joo, Young Hoon
• Is Part Of: IET control theory & applications. Volume 11:Issue 9(2017)
• Page Start: 1474
• Page End: 1484
• Publication Date: 2017-06-01
• Subjects: sampled data systems -- delays -- H∞ control -- continuous time systems -- uncertain systems -- time‐varying systems -- Lyapunov methods -- stability; input‐delay approach -- polynomial sampled‐data control systems -- H∞ stabilisation condition -- sum‐of‐square analysis -- external disturbance -- continuous‐time variables -- sampled state variables -- mixed‐states problem -- time‐varying uncertainty -- polynomial time‐dependent Lyapunov‐Krasovskii functional -- numerical solvers -- slack variables; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2016.1037
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : In this study, the authors develop an H ∞ 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.