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In many industrial applications, the existing constraints mandate the use of controllers of low and fixed order while typically, modern methods of optimal control produce high-order controllers. Structure and Synthesis of PID Controllers seeks to start to bridge the resultant gap and presents a novel methodology for the design of low-order controllers such as those of the P, PI and PID types. Written in a self-contained and tutorial fashion, this research monograph first develops a fundamental result, generalizing a classical stability theorem–the Hermite–Biehler Theorem–and then applies it to designing controllers that are widely used in industry. It contains material on:• current techniques for PID controller design;• generalization of the Hermite-Biehler theorem;• stabilization of linear time-invariant plants using PID controllers;• optimal design with PID controllers;• robust and non-fragile PID controller design;• stabilization of first-order systems with time delay;• constant-gain stabilization with desired damping• constant-gain stabilization of discrete-time plants. Practitioners, researchers and graduate students should find this book a valuable source of information on cutting-edge research in the field of control.