A Computational Method for Optimal H_∞ Norm of LTV Systems (State Feedback Case)

The aim of this paper is to propose a new method for the optimal "H_∞ norm" computation of time-varying systems. When we define the L_2-induced norm as "H- norm", the optimal "H_∞ norm" computation problem can be formulated as a minimax problem involving control and exogenous inputs. Our approach is as follows. First, we derive analytical solutions for the minimax problems with the exogenous inputs being frozen. Secondly, we present an algorithm for numerical solutions of the minimax problem with the control being frozen : Here, we prove that accumulation points generated by the algorithm satisfy the necessary conditions for optimality. Thirdly, combining the two above-mentioned techniques, we propose a relatively simple method for minimax solutions under assumptions that the saddle points exist. Lastly, we demonstrate the effectiveness of our approach by some simulations