TY - JOUR
T1 - High order sliding mode observer for linear systems with unbounded unknown inputs
AU - Bejarano, Francisco J.
AU - Fridman, Leonid
N1 - Funding Information:
Francisco J. Bejarano thanks the support given by the Mexican CONACyT postdoctoral grant CVU 103957. Both authors acknowledge the Mexican CONACyT project 56819 and PAPIIT 111208.
PY - 2010/9
Y1 - 2010/9
N2 - A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is generated in order to fulfil, what we will call, the Hautus condition, which finally allows decomposing the system, in new coordinates, into two subsystems; the first one being unaffected directly by the unknown inputs, and the state vector of the second subsystem is obtained directly from the original system output. Such decomposition permits designing of a Luenberger observer for the first subsystem, which satisfies the Hautus condition, i.e. all the outputs have relative degree one w.r.t. the unknown inputs. This procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible. Simulations are given in order to show the effectiveness of the proposed observer.
AB - A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is generated in order to fulfil, what we will call, the Hautus condition, which finally allows decomposing the system, in new coordinates, into two subsystems; the first one being unaffected directly by the unknown inputs, and the state vector of the second subsystem is obtained directly from the original system output. Such decomposition permits designing of a Luenberger observer for the first subsystem, which satisfies the Hautus condition, i.e. all the outputs have relative degree one w.r.t. the unknown inputs. This procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible. Simulations are given in order to show the effectiveness of the proposed observer.
KW - sliding mode observer
KW - strong detectability
KW - unknown inputs
UR - http://www.scopus.com/inward/record.url?scp=77955974100&partnerID=8YFLogxK
U2 - 10.1080/00207179.2010.501386
DO - 10.1080/00207179.2010.501386
M3 - Artículo
SN - 0020-7179
VL - 83
SP - 1920
EP - 1929
JO - International Journal of Control
JF - International Journal of Control
IS - 9
ER -