Name
Title | ||
|---|---|---|
Robust analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs |
Abstract | ||
|---|---|---|
A particular class of uncertain linear discrete-time periodic systems is considered. The problem of robust stabiliza- tion of real polytopic linear discrete-time periodic systems via a periodic state-feedback law is tackled here. Using additional slack variables and the periodic Lyapunov lemma, an extended sufficient condition of robust stabilization is proposed. Based on periodic parameter-dependent Lyapunov functions, this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework. This is illustrated on numerical examples from the literature. extrapolated from the LTI set-up. Structural properties, sta- bility analysis as well as the most popular synthesis tech- niques (pole placement, Linear Quadratic optimal control) were therefore extended to discrete-time and continuous-time periodic systems (6), (2), (7), (27), (27). Surprisingly, few results exist that extend the robust control framework to periodic systems. (12), (24), (14). In this paper, a particular class of uncertain linear discrete- time periodic systems similar to the one presented in (24), is considered. The problem of robust stabilization of real polytopic linear discrete-time periodic systems via a perio- dic state-feedback law is tackled here. As the usual lifted representations of the periodic systems naturally lead to hard numerical computations due to the sparse and highly structu- red matrices involved (15), a more straightforward approach based on the periodic Lyapunov lemma (1) is developed here. Using additional slack variables already introduced in the robust LTI context (11), (19), (20), an extended suffi- cient condition of robust stabilization is proposed. Based on periodic parameter-dependent Lyapunov functions, this last condition is shown to be always less conservative than the more classic one based on the quadratic stability framework and proposed in (24). Two numerical examples illustrate the |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/CDC.2005.1583077 | Conference on Decision and Control |
Keywords | DocType | ISSN |
control systems,robustness,stability,symmetric matrices,control theory,discrete time | Conference | 0191-2216 |
ISBN | Citations | PageRank |
0-7803-9567-0 | 14 | 1.14 |
References | Authors | |
8 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| denis arzelier | 1 | 14 | 1.14 |
| dimitri peaucelle | 2 | 14 | 1.14 |
| christophe farges | 3 | 14 | 1.14 |
| jamal daafouz | 4 | 14 | 1.14 |