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Control and Stability Analyzing of the Time-Delay Systems with Time-Varying Delays

Systems with delays are a specific group of dynamic systems. The fact that some delays can be short and some can be long makes system analysis and control design much more complex. In this paper we present a proposal to solve the problem of stability and control design of continuous time systems with time-varying delays. Based on the Lyapunov-Krasovskii functional the stability condition is derived using the linear matrix inequality (LMI) techniques, and convex optimization principle to find LMI variables which simultaneously satisfies the limitations given by the theory of Lyapunov-Krasovskii functionals. Obtained solution is the feasible convex LMI problem for the static controller design. Finally the design method is demonstrated using a system model example.