Decentralized Stabilization of Interconnected Systems With Time-Varying Delays TeX Export

@article{citeulike:6038543, abstract = {<para> This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an <formula formulatype="inline"><tex Notation="TeX">\$gamma\$</tex> </formula>-level <formula formulatype="inline"><tex Notation="TeX">\${cal L}\_{2}-gain\$</tex></formula>. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed <formula formulatype="inline"><tex Notation="TeX">\$gamma\$</tex></formula>-level <formula formulatype="inline"><tex Notation="TeX">\${cal L}\_{2}\$</tex></formula> gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example. </para>}, author = {Mahmoud, M. S.}, citeulike-article-id = {6038543}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TAC.2009.2031572}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5286276}, day = {13}, doi = {10.1109/TAC.2009.2031572}, journal = {Automatic Control, IEEE Transactions on}, keywords = {switching}, month = {October}, number = {11}, pages = {2663--2668}, posted-at = {2009-10-30 01:36:13}, priority = {2}, title = {Decentralized Stabilization of Interconnected Systems With Time-Varying Delays}, url = {http://dx.doi.org/10.1109/TAC.2009.2031572}, volume = {54}, year = {2009} }

TY - JOUR ID - citeulike:6038543 L3 - citeulike-article-id:6038543 N2 - <para> This technical note establishes decentralized delay-dependent stability and stabilization methods for two classes of interconnected continuous-time systems. The two classes cover the linear case and the Lipschitz-type nonlinear case. In both cases, the subsystems are subjected to convex-bounded parametric uncertainties and time-varying delays within the local subsystems and across the interconnections. An appropriate Lyapunov functional is constructed to exhibit the delay-dependent dynamics at the subsystem level. In both cases, decentralized delay-dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)-based conditions under which every local subsystem of the linear interconnected delay system is robustly asymptotically stable with an <formula formulatype="inline"><tex Notation="TeX">$gamma$</tex> </formula>-level <formula formulatype="inline"><tex Notation="TeX">${cal L}_{2}-gain$</tex></formula>. Then we design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent asymptotic stability with a prescribed <formula formulatype="inline"><tex Notation="TeX">$gamma$</tex></formula>-level <formula formulatype="inline"><tex Notation="TeX">${cal L}_{2}$</tex></formula> gain for each subsystem. The decentralized feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example. </para> IS - 11 JF - Automatic Control, IEEE Transactions on EP - 2668 TI - Decentralized Stabilization of Interconnected Systems With Time-Varying Delays VL - 54 SP - 2663 KW - switching AU - Mahmoud, MS PY - 2009/10/13/ UR - http://dx.doi.org/10.1109/TAC.2009.2031572 ER -