Optimal guaranteed cost control of a class of discrete-time nonlinear systems with Markovian switching and mode-dependent mixed time delays
Journal article, Peer reviewed
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Original versionLiu, Y., Karimi, H. R., & Liu, X. (2013). Optimal guaranteed cost control of a class of discrete-time nonlinear systems with Markovian switching and mode-dependent mixed time delays. Abstract and Applied Analysis, 2013. doi: 10.1155/2013/653628 10.1155/2013/653628
The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/653628 Open Access