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State Feedback Stabilization of Switched Systems with Delay: Trajectory Based Approach

Frédéric Mazenc 1 Saeed Ahmed 2 Hitay Ozbay 2
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : We present a new trajectory based approach for state feedback stabilization of switched linear continuous-time systems with a time-varying input delay. In contrast with finding classical common Lyapunov function or multiple Lyapunov functions for establishing the stability of the closed-loop switched system, the new trajectory based approach relies on verifying certain inequalities along the solution of a supplementary system. This study does not make any assumption regarding the stabi-lizability of all of the constituent modes of the switched system. Moreover, no assumption is needed about the differentiability of the delay and no constraint is imposed on the upper bound of the delay derivative. Finally, an illustrative example is included to illustrate the applicability of our results.
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Frédéric Mazenc, Saeed Ahmed, Hitay Ozbay. State Feedback Stabilization of Switched Systems with Delay: Trajectory Based Approach. IEEE American Control Conference (ACC) 2017, May 2017, Seattle, United States. pp.4540-4543, ⟨10.23919/ACC.2017.7963655⟩. ⟨hal-01660129⟩

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