A QUADRATIC-PROGRAMMING APPROACH FOR SOLVING THE L(1) MULTIBLOCK PROBLEM

The authors present a new method to compute solutions to the general m ultiblock l(1) control problem. The method is based on solving a stand ard H-2 problem and a finite-dimensional semidefinite quadratic progra mming problem of appropriate dimension. The new method has most of the properties that separately characterize many existing approaches. In particular, as the dimension of the quadratic programming problem incr eases, this method provides converging upper and lower bounds on the o ptimal it norm and, for well posed multiblock problems, ensures the co nvergence in norm of the suboptimal solutions to an optimal l(1) solut ion. The new method does not require the computation of the interpolat ion conditions, and it allows the direct computation of the suboptimal controller.