H _∞ Control Problem of Discrete 2-D Switched Mixed Delayed Systems Using the Improved Lyapunov-Krasovskii Functional

This paper deals with the problem of exponential stability and H_∞ control of two-dimensional (2-D) switched discrete systems with mixed time-varying delays. Firstly, this work suggests some improvements to Lyapunov-Krasovskii functional (LKF) discussed in the previous literature. Such improvements have been achieved by introducing some new terms containing the summations of state vector in single and double forms in an effort to capture the extra information related to time delays. Secondly, delay-dependent conditions based on the improved LKF are derived for the exponential stability and H_∞ performance of 2-D switched systems in the form of linear matrix inequalities (LMIs) by virtue of the average dwell time approach. Thirdly, a state-feedback controller is designed to ensure the exponential stability of the overall closed-loop system under consideration with a desirable H_∞ disturbance attenuation level γ. Finally, a suitable example is provided which highlights the benefits of the proposed results by comparing them with the results available in literature both in terms of conservativeness and computational burden.