H2 and H∞ Control for Multivariable Systems


The frequency-domain data of a multivariable systems in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parameterized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like H2 and H and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex–concave optimization problem and then convexified by linearisation of the concave part around an initial controller. The performance criterion converges monotonically to a local optimum or a saddle point in an iterative algorithm. 


A data-driven approach to robust control of multivariable systems by convex optimization, A Karimi, C Kammer, Automatica 85, 227-233, 2017.