TY - JOUR
T1 - Unconstrained and constrained stabilisation of bilinear discrete-time systems using polyhedral Lyapunov functions
AU - Athanasopoulos, Nikolaos
AU - Bitsoris, George
PY - 2010
Y1 - 2010
N2 - The constrained and unconstrained stabilisation problem of discrete-time bilinear systems is investigated. Using polyhedral Lyapunov functions, conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second-order polynomial nonlinearities are first established. Then, systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented. Attention is drawn to the case where no linear control law rendering the pre-specified desired domain of attraction positively invariant exists. For this case, an approach guaranteeing the existence of a possibly suboptimal solution is established.
AB - The constrained and unconstrained stabilisation problem of discrete-time bilinear systems is investigated. Using polyhedral Lyapunov functions, conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second-order polynomial nonlinearities are first established. Then, systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented. Attention is drawn to the case where no linear control law rendering the pre-specified desired domain of attraction positively invariant exists. For this case, an approach guaranteeing the existence of a possibly suboptimal solution is established.
U2 - 10.1080/00207179.2010.531396
DO - 10.1080/00207179.2010.531396
M3 - Article
SN - 0020-7179
VL - 83
SP - 2483
EP - 2493
JO - International Journal of Control
JF - International Journal of Control
IS - 12
ER -