Optimal Guaranteed Cost Control of a Class of Discrete‐Time Nonlinear Systems with Markovian Switching and Mode‐Dependent Mixed Time Delays

Yurong Liu, Hamid Reza Karimi and Xiaohui Liu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/653628

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:653628

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