IEEE Transactions on Automatic Control, Vol.43, No.10, 1501-1505, 1998
Multivariable pi-sharing theory and its application on the Lur'e problem
In this paper the pi-sharing theory developed of Lawrence and Johnson is extended to handle square multivariable continuous-time systems, and for the most essential part of finding usable pi-coefficients, LMI formulations are utilized such that for any finite-dimensional LTI systems, time-invariant pi-coefficients can be obtained easily. Furthermore, pi-coefficients are derived for sector-hounded nonlinearities, and the extended pi-sharing theory is applied to the multivariable Lur'e problem, With this approach, not only can a Lur'e system with known sector bounds on nonlinearities be checked for stability, but also the maximal bounds ensuring stability can be found under some conditions.