A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems

Abstract

This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMIs are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMIs carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMIs are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMIs leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMIs enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.