H-2 OPTIMAL-CONTROL WITH AN ALPHA-SHIFTED POLE CONSTRAINT

Modified Lyapunov equations for regional pole constraints in H-2 synth esis have been considered in recent papers. This approach involves a c onstraint equation for enforcing the pole constraints and leads to an auxiliary cost that overbounds the original H-2 performance. The auxil iary cost can then be used for optimization with respect to the modifi ed Lyapunov equations that characterize the constraint region. In this paper, we consider an alpha-shifted constraint region and show that a n augmented system whose order is twice that of the original system ca n be constructed to eliminate the need for an overbound so that exact H-2 cost optimization can be performed. This augmented system is then utilized for closed-loop controller synthesis within a decentralized s tatic output feedback setting. The construction of the augmented syste m is a refinement of the approach of Gu et al. (1992). A numerical alg orithm based upon the BFGS quasi-Newton method is used for computing t he optimal controller gains. The numerical results are compared to the classical exponential cost weighting technique of Anderson and Moore (1989).