On enhanced mixed H2/H∞ design conditions for control of linear time-invariant systems

The paper provides a new modification of the enhanced linear matrix inequality (LMI) conditions for the mixed H
₂
/H
_∞
control design, where the H
_∞
and H
₂
strategies are combined as a mixed control problem. The goal of this problem is to design the static feedback controller which guarantees not only a pre-specified H∞ norm disturbance attenuation level, but also the minimum H
₂
performance index. Analyzing sets of performance specifications given on the mixed H
₂
/H
_∞
control strategy, the main advantage is that can formulated as a minimization problem subject to convex constraints expressed by a system of LMIs. An enhanced algorithm is provided to guaranty asymptotic stability of the closed-loop control structure and to define the controller parameter design conditions. The feasibility and the effectiveness of the mixed control strategy are demonstrated by a numerical example. Applied enhanced design conditions give a generalized framework of control design for linear time-invariant system, where the corresponding LMIs are in full generality.