Performance requirements and design limitations
In this chapter, we consider briefly some important issues concerning the performance requirements to closed-loop linear systems and the fundamental design limitations in achieving the control aims. The performance specifications are formulated in continuous-time due to the clear physical interpretation in this case. First, we present the relatively simple case of single-input-single-output (SISO) systems which are well studied in the classical control theory. The trade-offs in the design of such systems are shown in some details. Then, we discuss the more complicated case of multiple-input-multiple-output (MIMO) systems whose performance is investigated by using the singular value plots of certain closed-loop transfer function matrices. An important issue in controller design is the closed-loop system performance in presence of different uncertainties. At the end of the chapter, we present some elements of the contemporary approach to the robustness analysis of uncertain linear systems based on the small gain theorem and structured singular value (SSV).
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