Abstract
This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
| Original language | English |
|---|---|
| Pages (from-to) | 950-959 |
| Number of pages | 10 |
| Journal | International Journal of Control |
| Volume | 89 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - May 3 2016 |
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Keywords
- Hybrid systems
- piecewise-affine systems
- stability analysis
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
Cite this
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains. / Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto.
In: International Journal of Control, Vol. 89, No. 5, 03.05.2016, p. 950-959.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
AU - Rubagotti, Matteo
AU - Zaccarian, Luca
AU - Bemporad, Alberto
PY - 2016/5/3
Y1 - 2016/5/3
N2 - This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
AB - This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
KW - Hybrid systems
KW - piecewise-affine systems
KW - stability analysis
UR - http://www.scopus.com/inward/record.url?scp=84958766459&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958766459&partnerID=8YFLogxK
U2 - 10.1080/00207179.2015.1108456
DO - 10.1080/00207179.2015.1108456
M3 - Article
VL - 89
SP - 950
EP - 959
JO - International Journal of Control
JF - International Journal of Control
SN - 0020-7179
IS - 5
ER -