Robust stability using interval analysis

Abstract

In the context of linear time-invariant systems with structured uncertainties, a robust stability analysis performed with the aid of interval analysis tools is proposed. In particular, a characteristic polynomial is considered whose coefficients are nonlinear functions of physical uncertain parameters with known bounds. The analysis is centred on the computation of the robust decay rate which is the absolute value of the maximal real part of the characteristic roots for any possible value of the uncertain parameters. An interval algorithm converging with certainty is devised to compute arbitrarily good lower and upper bounds of the robust decay rate. The proposed approach to robust stability has the potential merit to permit dealing with a large class of characteristic coefficient functions which includes, for example, multivariate polynomials and transcendental functions. Worked examples with computational results are included