Upper bounds on the best achievable performance for time-weighted cost functionals

This paper focuses on the optimal control of LTI plants when a time-weighted performance measure is employed. Drawing on basic properties of indefinite inner product spaces, we derive an algorithm that iteratively refines an upper bound on the best achievable performance. Each step of the algorithm consist in solving a set of (non-coupled) Lyapunov equations and can thus be implemented using standard software. Expressions for the LTI controllers that attain performance levels equal to the proposed bounds are also provided.