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Improved State Feedback Controller Design Using Lyapunov-Krasovskii Functional for Linear Discrete Systems with time-delay

The work presented in this paper uses Lyapunov-Krasovskii Functional (LKF) to solve discrete-time system stabilization problem with time-varying delay. Invoking summation inequality and the extended reciprocally convex combinational lemma, forward difference of the chosen LKF is done to give a tighter estimate. To ensure asymptotic stability of the system in the sense of Lyapunov, a delay-dependent stability criteria is derived in the form of Linear Matrix Inequality (LMI). Finally, a numerical example is provided to demonstrate the applicability of developed theory.