A MULTIVARIABLE STABILITY MARGIN IN THE PRESENCE OF TIME-VARYING, BOUNDED RATE GAINS

In this paper we consider a MIMO asymptotically stable linear plant. F or such a system the classical concepts of quadratic stability margin and multivariable gain margin can be defined. These margins have the f ollowing interpretation: consider the closed-loop system composed of t he plant and several rear parameters, one inserted in each channel of the loop; then any time-varying (time-invariant) parameters whose ampl itudes are smaller than the quadratic stability (multivariable gain) m argin result in a stable closed-loop system. For time-varying paramete rs whose magnitudes are between these two stability measures, stabilit y may depend on the rate of variation of the parameters. Therefore it makes sense to consider the stability margin given by the maximal allo wable rate of variation of the parameters which guarantees stability o f the closed loop system. As shown in this paper, a lower bound on thi s margin can be obtained with the aid of parameter dependent Lyapunov functions.