A trust-region method for optimal H₂ model reduction of discrete-time dynamical systems

In this paper, we present an optimal H₂ model reduction method on the basis of the trust-region technique for linear time-invariant discrete-time dynamical systems. First, based on the poles and residues, the H₂ error norm for single-input and single-output discrete-time systems is investigated, which leads to the H₂ error gradient and Hessian. Next, for multiple-input and multiple-out discrete-time systems, the gradient and Hessian of the H₂ error norm are accordingly derived. Then, the H₂ error gradient and Hessian are employed to establish the trust-region method for optimal H₂ model reduction. Moreover, it is shown that the proposed method can produce a decreasing sequence. The construction of the state space realization of the reduced order system is studied concerning the divisions of the resulting residues. Model reduction is investigated for nonlinear discrete-time system. Finally, an illustrative example is used to demonstrate the performance.