Abstract
A control system is robust if it remains stable and meets certain performance criteria in the presence of possible uncertainties as discussed in Chap. 2. The robust design is to find a controller, for a given system, such that the closed-loop system is robust. The \(\mathcal{H}_{\infty}\) optimization approach, being developed in the last two decades and still forming an active research area, has been shown to be an effective and efficient robust design method for linear, time-invariant control systems. In the previous chapter, various robust stability considerations and nominal performance requirements were formulated as a minimization problem of the infinitive norm of a closed-loop transfer function matrix. Hence, in this chapter, we shall discuss how to formulate a robust design problem into such a minimization problem and how to find the solutions. The \(\mathcal{H}_{\infty}\) optimization approach solves, in general, the robust stabilization problems and nominal performance designs.
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Gu, DW., Petkov, P.H., Konstantinov, M.M. (2013). \(\mathcal{H}_{\infty}\) Design. In: Robust Control Design with MATLAB®. Advanced Textbooks in Control and Signal Processing. Springer, London. https://doi.org/10.1007/978-1-4471-4682-7_4
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DOI: https://doi.org/10.1007/978-1-4471-4682-7_4
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