By Noyes A.A., Beckman A.O.

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This problem arose directly from his work on the problems of long-distance telephony. This was soon followed by the work of Bode [42] 19 Sec. 2. HISTORICAL BACKGROUND which eventually led to the introduction of the notions of gain and phase margins for feedback systems. Nyquist's criterion and the concepts of gain and phase margin form the basis for much of the classical control system design methodology and are widely used by practicing control engineers. The next major period in the evolution of control theory was the period between 1960 and 1975 when the state-variable approach and the ideas of optimal control in the time-domain were introduced.

These BACKGROUND AND MOTIVATION Ch. 0 28 line segments, labeled extremal segments, play a fundamental characterizing role in later chapters. In Chapter 8 we develop some extremal frequency domain properties of linear interval control systems. The extremal segments are shown to possess bound- frequency domain templates Nyquist, Bode and Nichols envelopes of linear interval systems. The extremal gain and phase margins of these systems occur on these segments. ary properties that are useful for generating the and the We show how these concepts are useful in extending classical design techniques to linear interval systems by giving some examples of control design.

Therefore the standard machinery can be used to determine whether a robustly stabilizing compensator exists within the family of compensators that stabilize G0 (s). From the above discussion it is clear that in the norm-bounded formulation robust stability and robust performance problems are closely related. 8 Theory The objective of theory is to rene the small gain condition derived in H1 optimal control, by imposing constraints on the perturbation structure allowed and thus derive robustness results for a more realistic problem.