Robust Fixed-Order Controller Design with Common Lyapunov Strictly Positive Realness Characterization

This paper investigates the design of a robust fixed-order controller for a polytopic system with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the performance specifications on sensitivity shaping are conformed in a specific finite frequency range. Utilizing the notion of common Lyapunov strictly positive realness (CL-SPRness), the equivalence between strictly positive realness (SPRness) and strictly bounded realness (SBRness) is elegantly established; and then the specifications on robust stability and performance are transformed into the SPRness of newly constructed systems and further characterized in the framework of linear matrix inequality (LMI) conditions. Compared with the traditional robust controller synthesis approaches, the proposed methodology here avoids the tedious yet mandatory evaluations of the specifications on all vertices of the polytopic system; only a one-time checking of matrix existence is needed exclusively, and thus the typically heavy computational burden involved (in such robust controller design problems) is considerably alleviated. Moreover, it is noteworthy that the proposed methodology additionally provides essential necessary and sufficient conditions for this robust controller design with the consideration of a prescribed finite frequency range; and therefore significantly less conservatism is attained in the system performance.Comment: 10 pages, 6 figure

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This paper presents the synthesis of an optimal robust controller with the use of pole placement technique. The presented method includes solving a polynomial equation on the basis of the chosen fixed characteristic polynomial and introduced parametric solutions with a known parametric structure of the controller. Robustness criteria in an unstructured uncertainty description with metrics of norm ℋ∞ are for a more reliable and effective formulation of objective functions for optimization presented in the form of a spectral polynomial with positivity conditions. The method enables robust low-order controller design by using plant simplification with partial-fraction decomposition, where the simplification remainder is added to the performance weight. The controller structure is assembled of well-known parts such as disturbance rejection, and reference tracking. The approach also allows the possibility of multiobjective optimization of robust criteria, application of mixed sensitivity problem, and other closed-loop limitation criteria, where the common criteria function can be composed from different unrelated criteria. Optimization and controller design are performed with iterative evolution algorithm