ITSE optimal controller design and achievable performance bounds

This article proposes a methodology to design optimal controllers and to compute achievable performance bounds in the control of linear, stable discrete-time SISO plants. The performance is measured using a time-weighted cost function (ITSE) of the tracking error for a step reference or a step output disturbance, combined with a measure of the energy of the incremental control. The proposed methodology relies on the use of a function space product that, for stable systems, can be defined in both the frequency and the time-domains. The solution technique requires the expansion of stable functions in orthogonal basis. An analytical expression is found for the computation of the optimal coefficients of the expansion. Numerical examples are included to illustrate the results.