Computation of performance robustness bounds for control systems with parameter uncertainties: an LMI approach

The problem of computing an upper bound on the size of parameters to guarantee the β-boundedness of control systems with parametric uncertainties is focused. Based on an improved linear matrix inequality (LMI) representation of β-boundedness criteria for polytopic uncertain systems, this problem is transformed into a generalised eigenvalue problem, which can be easily tested with efficient LMI algorithms. Results are proved to be less conservative than those results based on the classical β-bounded criterion. Two numerical examples are given to illustrate the results.