A multivariable stability margin in the presence of time-varying, bounded rate gains.

In this paper we consider a MIMO asymptotically stable linear plant. For such a system the classical con- cepts of quadratic stability margin and multivariable gain margin can be dened. These margins have the following interpretation: consider the closed-loop system composed of the plant and several real parameters, one inserted in each channel of the loop; then any time-varying (time-invariant) parameters whose amplitudes are smaller than the quadratic stability (multivariable gain) margin result in a stable closed-loop system. For time-varying parameters whose magnitudes are between these two stability measures, stability may depend on the rate of variation of the parameters. Therefore it makes sense to consider the stability margin given by the maximal allowable rate of variation of the parameters which guarantees stability of the closed loop system. As shown in this paper, a lower bound on this margin can be obtained with the aid of parameter dependent Lyapunov functions