State bounds estimation for nonlinear systems using μ-analysis

Developing state bound estimation algorithms for nonlinear systems has been of high importance in robustness analysis of dynamic systems. For many cases, Monte-Carlo simulation might be the only tool to estimate these bounds for a general type of nonlinear systems. The required number of simulations for a tight bound, however, would be very large and it might be impossible to complete within a given computation time. β-formulation for state bounds transforms the bound estimation problem to a singularity problem and the singular problem is solved using a randomised optimisation approach. The performance of the algorithms are demonstrated by a simple discrete system; large-scale biological systems; and a hybrid system.