A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems

This paper addresses robust performance analysis problems for linear time-invariant systems depending on uncertain parameters. It is well known that, in the case of affine parameter dependence, we can deal with such problems based on standard LMI (Linear Matrix Inequalities) characterizations and the concept of quadratic stability. However, in the case of rational parameter dependence, we need another effort to arrive at numerically tractable conditions. This paper clarifies that recently developed dilated LMI characterizations are useful in dealing with such robust performance analysis problems. The dilated LMI’s also allow us to employ parameter-dependent Lyapunov variables, which are known to be quite effective to reduce the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.