Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach | Zendy

Valter J. S. Leite | Zendy; Márcio F. Miranda | Zendy

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Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

Author(s) -

Valter J. S. Leite,

Márcio F. Miranda

Publication year - 2008

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2008/875609

Subject(s) - linear matrix inequality , control theory (sociology) , mathematics , discrete time and continuous time , stability (learning theory) , regular polygon , class (philosophy) , convex optimization , state (computer science) , mathematical optimization , computer science , algorithm , control (management) , statistics , geometry , artificial intelligence , machine learning

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions

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