On Robust Stability and Performance With a Fixed-Order Controller Design for Uncertain Systems

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 article provides an essential basis for the design of a fixed-order controller for a system with bounded parametric uncertainties, which avoids the tedious but necessary evaluations of the specifications on all the extreme models in an explicit manner. 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 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. Furthermore, the conditions for robust stability and performance are expressed in the framework of linear matrix inequality (LMI) constraints, and thus can be efficiently solved. Comparative simulations are provided to demonstrate the effectiveness and efficiency of the proposed approach.