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Robust stability and stabilisation of uncertain switched linear discrete time-delay systems

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3 Author(s)
Zhang, L. ; Ecole Polytech. de Montreal, Montreal, QC ; Shi, P. ; Basin, M.

The robust stability and stabilisation problems for switched linear discrete-time systems are studied. The parameter uncertainties in the system under consideration are time-varying but norm-bounded, and the time delay is assumed to be time-varying and bounded, which covers the constant and mode-dependent constant delays as special cases. First, sufficient conditions are derived to guarantee the stability of the uncertain system. Then, a control law is designed so that the resulting closed-loop system is stable for all admissible uncertainties. A linear matrix inequality approach, together with a cone complementary linearisation algorithm, is proposed to solve the above problems. A numerical example is given to show the potential applicability of the obtained theoretic results.

Published in:

Control Theory & Applications, IET  (Volume:2 ,  Issue: 7 )