State bounds estimation for nonlinear systems using μ-analysis ?

Developing estimation algorithms for state bounds of nonlinear systems has been of high importance in robustness analysis for various systems including engineering systems and biological systems. For many cases, Monte-Carlo simulation might be the only tool to estimate these bounds for a general type of nonlinear systems. In order to obtain tight bounds the number of required simulations would be very large and it may not be able to perform so many simulations for some systems in a given computation time. Recently, a state bound estimation algorithm using μ-formulation presents a promising result in terms of computational efficiency and providing very tight bounds. By combining the μ-formulation for state bounds with a geometrical interpretation of μ-analysis, the algorithm is extended to estimate state bounds for general types of nonlinear systems. The performance of the algorithms are demonstrated by a simple discrete system; large-scale biological systems; and a hybrid system.