TY - CHAP
T1 - Stability and Controller Synthesis of Discrete Linear-Switched Systems
AU - Gershon, Eli
AU - Shaked, Uri
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019
Y1 - 2019
N2 - Sufficient conditions are presented for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic-type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterward. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case, where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2 -gain analysis where a bounded real lemma is derived, and to H∞ control and estimation, both for the nominal and the uncertain cases.
AB - Sufficient conditions are presented for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic-type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterward. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case, where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l2 -gain analysis where a bounded real lemma is derived, and to H∞ control and estimation, both for the nominal and the uncertain cases.
UR - http://www.scopus.com/inward/record.url?scp=85066747873&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-16008-1_6
DO - 10.1007/978-3-030-16008-1_6
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AN - SCOPUS:85066747873
T3 - Lecture Notes in Control and Information Sciences
SP - 75
EP - 92
BT - Lecture Notes in Control and Information Sciences
PB - Springer Verlag
ER -