Robust analysis of linear systems affected by time-invariant hypercubic parametric uncertainty

In this paper, a new technique for establishing the stability of a linear system polynomially affected by time-invariant uncertainty constrained in a hypercube is presented for both continuous-time and discrete-time case. Specifically, a necessary and sufficient condition not based on the use of Lyapunov functions and checkable through LMIs is provided. The contribution of this technique with respect to existing approaches that provide necessary and sufficient conditions for establishing the stability consists of a significantly smaller computational burden in quite frequent cases.