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Achievable performance bound for ITSE optimal controller design

This paper proposes a methodology 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) that quantifies the control error for a step reference or a step output disturbance. The proposed methodology relies on the use of a function space product that, for stable systems, can be defined in both frequency and time domain. The solution technique requires the expansion of stable functions in orthogonal series. An analytical expression is found for the computation of the optimal coefficients of the expansion. Numerical examples are given to illustrate the results.