access icon free Input-delay approach to sampled-data control of polynomial systems based on a sum-of-square analysis

© The Institution of Engineering and Technology
Received 05/08/2016, Accepted 16/01/2017, Revised 06/01/2017, Published 06/02/2017

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.

Inspec keywords: continuous time systems; delays; uncertain systems; sampled data systems; H∞ control; Lyapunov methods; time-varying systems; stability

Other keywords: mixed-states problem; polynomial time-dependent Lyapunov-Krasovskii functional; numerical solvers; sampled state variables; sum-of-square analysis; external disturbance; input-delay approach; time-varying uncertainty; H∞ stabilisation condition; continuous-time variables; slack variables; polynomial sampled-data control systems

Subjects: Time-varying control systems; Stability in control theory; Discrete control systems; Optimal control; Distributed parameter control systems

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