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