Q-domain four-blocks l1-optimal control design for SISO plants

The multiblock l₁-optimal control problem for single-input single-output (SISO) plants is considered. It is shown that it can be converted via polynomial equation techniques to an infinite-dimensional linear programming (LP) problem. Finite dimensional sub/super approximations can be determined by considering two sequences of modified finite-dimensional linear programming problems derived directly from the YJBK parameterisation by exploiting the underlying algebraic structure. This approach induces the application of a consistent truncation strategy that leads to a redundancy-free constraint formulation and, as a consequence, to linear programming problems less affected by degeneracy. Further, more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided, allowing the development of a simple and conceptually attractive theory.