  Typically, it is desirable to design a control system that is not only
robustly stable in the presence of parametric uncertainties but also guarantees
an adequate level of system performance. However, most of the existing methods
need to take all extreme models over an uncertain domain into consideration,
which then results in costly computation. Also, since these approaches attempt
(rather unrealistically) to guarantee the system performance over a full
frequency range, a conservative design is always admitted. Here, taking a
specific viewpoint of robust stability and performance under a stated
restricted frequency range (which is applicable in rather many real-world
situations), this paper provides an essential basis for the design of a
fixed-order controller for a system with bounded parametric uncertainties. A
Hurwitz polynomial is used in the design and the robust stability is
characterized by the notion of positive realness, such that the required robust
stability condition is then suitably successfully constructed. Also, the robust
performance criteria in terms of sensitivity shaping under different frequency
ranges are constructed based on an approach of bounded realness analysis.
Necessary and sufficient conditions are provided for both the robust stability
and robust performance criteria. Furthermore, these conditions are expressed in
the framework of linear matrix inequality (LMI) constraints, and thus can be
efficiently solved. Comparative simulations are provided to illustrate the
effectiveness and efficiency of the proposed approach.
