Finite horizon robustness analysis of LTV systems using integral quadratic constraints

Worst-Case Disturbances for Time-Varying Systems with Application to Flexible Aircraft

“…The issues associated with the simulation of the Hamiltonian have been considered in the literature [12,13], but in this work a dierent approach is taken which exploits the structure of the worst-case signal and the properties of the solution Y . This paper is also closely related to a recent work [11] where a mathematical framework for nite horizon analysis of uncertain LTV systems was proposed. Robust performance of a nominal LTV system interconnected with an uncertain operator, which may model nonlinearities and dynamic or parametric uncertainty, was studied by leveraging the Integral Quadratic Constraints paradigm.…”

“…3.7.4 in [10] for the particular case of J corresponding to the induced L 2 gain. A statement and proof for general (Q,S,R,F ) cost functions can be found in [11]. Theorem 1 allows to assess the performance of the nite-horizon LTV system in Eq.…”

“…A two-point boundary value problem is used in the proof of Theorem 1 [10,11]. This section briey reviews a related useful result.…”

“…The construction builds on known results from the optimal control literature [10], which are reviewed in Section II. Specically, the paper uses a generalization of the strict bounded real lemma [10,11] stating an equivalence between a bound on a generic cost function J and the existence of a solution Y to a Riccati Dierential Equation (RDE). Examples for the L 2 and L 2 -to-Euclidean gains show that generic performance metrics can be specied by properly dening J.…”

Finite Time Robust Control of the Sit-to-Stand Movement for Powered Lower Limb Orthoses

“…where α ∈ [0, 1] weights the induced gains at an intermediate time t m and a final time t f . To calculate the induced gains we use the computational approach from [12] and the toolbox documented in [11].…”