New robust stability and performance conditions based on parameter dependent multipliers

This paper introduces a new robust stability and performance characterization for parameter dependent systems. The main idea is to jointly use parameter dependent Lyapunov functions and parameter dependent multipliers. It is shown that the novel tests can be easily specialized to the results that have been recently proposed in the literature and that have been derived in an independent fashion for discrete- and continuous-time systems. It is revealed that these characterization apply to system descriptions with rational parameter dependence, and we discuss in how far they extend to robust state-feedback controller synthesis. Various examples demonstrate the benefit of the proposed algorithms over previous approaches.