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Delay-Dependent Positivity and Stability Analysis of Discrete-Time Systems With Delay

In this letter, delay-dependent positivity and stability conditions, which are crucially different from existing delay-independent ones, are derived for discrete-time systems with time-varying delay. By utilizing a special property called non-oscillatory behavior of solutions of scalar difference equations with delays, the proposed conditions are formulated in terms of linear programming settings. The efficiency of the obtained results is illustrated by a numerical example with simulations.