Stability and dynamic performance bounds for nonlinear multivariable systems

Earlier work on sector bounded nonlinear multivariable systems has provided dynamic performance bounds on system response, via an element-by-element L¿¿ treatment. However, this approach relies on a stability criterion which is potentially very conservative, since it ignores both frequency dependence and phase interrelationships. In the paper, we use L2 vector norms in conjunction with nonsimilarity scaling to retrieve this information, and hence to derive a significantly improved stability condition. By the introduction of exponential weighting, it is then shown that the L2 stability result may be used to establish absolute bounds on system performance.