Abstract
In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance.
| Original language | English |
|---|---|
| Title of host publication | 2016 American Control Conference, ACC 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 5638-5643 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781467386821 |
| DOIs | |
| Publication status | Published - Jul 28 2016 |
| Externally published | Yes |
| Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016 |
Publication series
| Name | Proceedings of the American Control Conference |
|---|---|
| Volume | 2016-July |
| ISSN (Print) | 0743-1619 |
Conference
| Conference | 2016 American Control Conference, ACC 2016 |
|---|---|
| Country | United States |
| City | Boston |
| Period | 7/6/16 → 7/8/16 |
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All Science Journal Classification (ASJC) codes
- Electrical and Electronic Engineering
Cite this
Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles. / Ebihara, Yoshio; Shintani, Shogo; Hagiwara, Tomomichi.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 5638-5643 7526554 (Proceedings of the American Control Conference; Vol. 2016-July).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Dual LMI approach to H∞ performance limitations analysis of SISO systems with multiple unstable zeros and poles
AU - Ebihara, Yoshio
AU - Shintani, Shogo
AU - Hagiwara, Tomomichi
PY - 2016/7/28
Y1 - 2016/7/28
N2 - In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance.
AB - In this paper, we study a dual-LMI-based approach to H∞ performance limitations analysis of SISO systems with multiple (i.e., duplicated) unstable zeros and poles. The scope includes the analysis of the transfer functions M = (1+PK)-1 P, S = (1+PK)-1, and T = (1+PK)-1 PK where P and K stand for the plant and the controller, respectively. The latter two transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero of degree one or the sole unstable pole of degree one. However, such exact bounds are hardly available for the cases where the plant has multiple (i.e., duplicated) unstable zeros and poles. To obtain a lower bound of the best achievable H∞ performance for such involved cases, in this paper, we study a dual of the standard LMI that represents the existence of H∞ controllers achieving a prescribed H∞ performance level. By deriving a parametrization of dual feasible solutions and constructing a dual suboptimal solution analytically, we can readily obtain a lower bound of the best achievable H∞ performance.
UR - http://www.scopus.com/inward/record.url?scp=84992166061&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992166061&partnerID=8YFLogxK
U2 - 10.1109/ACC.2016.7526554
DO - 10.1109/ACC.2016.7526554
M3 - Conference contribution
AN - SCOPUS:84992166061
T3 - Proceedings of the American Control Conference
SP - 5638
EP - 5643
BT - 2016 American Control Conference, ACC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
ER -