Stability and performance bounds for the linearisation-based analysis and design of multivariable nonlinear systems

Abstract

The paper is concerned with the derivation of useful results that complement the linearisation-based analysis and design of multivariable systems with measurement nonlinearity. The approach is based on the closed-loop linearised system descriptions and certain nonlinearity related parameters representing sector and/or incremental sector properties, and also enables the consideration of nonlinearities with discontinuities at the origin. Nonlinear-system stability and performance is assessed on the basis of the stability and performance of the corresponding linearised system and certain easily computable sufficient conditions representing BIBO and asymptotic stability conditions, as well as absolute and derivative performance bounds. The results depend on useful linearised system descriptions such as the L∞ operator norm, thus offering the advantages of meaningful assessments and overall computational simplicity.