Multivariable tracking control for MIMO linear systems: an LMI approach

In this paper we consider the problem of achieving monotonic tracking control for multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems, from any initial condition. First, we show that this property is equivalent to achieving non-overshooting and non-undershooting starting from any initial condition. Second, we prove that a stable system is monotonic from every initial condition if and only if all the rows of the output matrix are left eigenvectors of the space transition matrix. In this way, the design of a controller which ensures global monotonic tracking can be reformulated as a convex optimization problem described by a set of Linear Matrix Inequalities (LMIs)