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Abstract: For linear systems with pointwise or distributed delay in the inputs which are stabilized through the reduction approach, we propose a new technique of construction of Lyapunov–Krasovskii functionals. These functionals allow us to establish the ISS property of the closed-loop systems relative to additive disturbances. [Copyright &y& Elsevier]

The PID control is favored in controlling industrial processes for its ease of implementation. In this paper we present an analytical study, with an aim at stability robustness, tracking performance, and pole placement of first-order unstable plants under PID control. We employ a multiplicity-induced dominancy (MID) strategy to design and tune PID controller gains, which is shown to possess desirable properties that ensure specified decay rate of the closed-loop response and the stability robustness of the closed-loop system in spite of variations in the delay parameter. We also study the tradeoff between delay robustness and tracking performance of PID controllers. We show that under the constraint of steady-state tracking, the maximal delay robustness range can be computed by solving a unimodal pseudo-concave optimization problem. [ABSTRACT FROM AUTHOR]