Mixed H2/H∞ Strategy in Control Law Parameter Design for Linear Strictly Metzlerian Systems

Abstract

The paper provides linear matrix inequality conditions in mixed $\mathrm{H}_{2}/ \mathrm{H}_{\infty}$ control design for strictly Metzlerian linear systems. The goal of this formulation is to design the state controller guaranteing $\mathrm{H}_{\infty}$ norm disturbance attenuation and optimized H2 norm performance. The problem is formulated multi-objective, respecting the constraints implying from H2 and $\mathrm{H}_{\infty}$ fulfillment, as well as from the parameter constraints defined by the system matrix structures in the strictly Metzlerian system description. The design character guaranties asymptotic stability realized in a strictly Metzlerian closed-loop system form. It is shown that enhanced design conditions span such a synthesis framework for strictly Metzlerian linear system, where matrix variables take diagonal form.