TY - GEN
T1 - Stochastic Discrete-Time Systems with Delay - Robust Vertex-dependent H∞State-feedback Control
AU - Gershon, Eli
AU - Shaked, Uri
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/20
Y1 - 2018/8/20
N2 - The theory of stochastic state-multiplicative state-feedback control of retarded discrete-time systems is extended to the robust polytopic case, where a vertex-dependent approach is applied. The latter problem is solved by first deriving a stability condition for uncertain systems based on the application of the Finsler lemma to the studied systems, where a special Lyapunov function is applied to each vertex of the uncertainty polytope. Compared to the stability condition which is obtained by the quadratic approach where a single Lyapunov function is applied to the whole uncertainty polytope, the vertex-dependent approach achieves a significatively less-conservative result than the former approach. Based on the vertex-dependent stability condition, a robust bounded real lemma is derived and solved, leading to the solution of the state-feedback control for uncertain systems.
AB - The theory of stochastic state-multiplicative state-feedback control of retarded discrete-time systems is extended to the robust polytopic case, where a vertex-dependent approach is applied. The latter problem is solved by first deriving a stability condition for uncertain systems based on the application of the Finsler lemma to the studied systems, where a special Lyapunov function is applied to each vertex of the uncertainty polytope. Compared to the stability condition which is obtained by the quadratic approach where a single Lyapunov function is applied to the whole uncertainty polytope, the vertex-dependent approach achieves a significatively less-conservative result than the former approach. Based on the vertex-dependent stability condition, a robust bounded real lemma is derived and solved, leading to the solution of the state-feedback control for uncertain systems.
KW - Input-output
KW - Retarded discrete-time systems
KW - State-feedback H∞) control
UR - http://www.scopus.com/inward/record.url?scp=85053462587&partnerID=8YFLogxK
U2 - 10.1109/MED.2018.8442980
DO - 10.1109/MED.2018.8442980
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AN - SCOPUS:85053462587
SN - 9781538678909
T3 - MED 2018 - 26th Mediterranean Conference on Control and Automation
SP - 499
EP - 504
BT - MED 2018 - 26th Mediterranean Conference on Control and Automation
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 26th Mediterranean Conference on Control and Automation, MED 2018
Y2 - 19 June 2018 through 22 June 2018
ER -