New Bounds on Parameter Uncertainties for Robust Stability

The problem of robust stability in linear systems with parametric uncertainties is considered. A new method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values and consequently, the stable region in the parameter space is not necessarily symmetric with respect to the origin; furthermore, the uncertain parameters do not have to be linearly independent to each other.