Robustness analysis of linear time-varying systems with application to aerospace systems

In recent years significant effort was put into developing analytical worst-case analysis tools to supplement the Verification \& Validation (V\&V) process of complex industrial applications under perturbation. Progress has been made for parameter varying systems via a systematic extension of the bounded real lemma (BRL) for nominal linear parameter varying (LPV) systems to IQCs. However, finite horizon linear time-varying (LTV) systems gathered little attention. This is surprising given the number of nonlinear engineering problems whose linearized dynamics are time-varying along predefined finite trajectories. This applies to everything from space launchers to paper processing machines, whose inertia changes rapidly as the material is unwound. Fast and reliable analytical tools should greatly benefit the V\&V processes for these applications, which currently rely heavily on computationally expensive simulation-based analysis methods of full nonlinear models. The approach taken in this thesis is to compute the worst-case gain of the interconnection of a finite time horizon LTV system and perturbations. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQC). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory. This utilizes a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can then be efficiently solved using custom-tailored meta-heuristic (MH) algorithms. One of the developed algorithms is initially benchmarked against non-tailored algorithms, demonstrating its improved performance. A second algorithm's potential application in large industrial problems is shown using the example of a touchdown constraints analysis for an autolanded aircraft as was as an aerodynamic loads analysis for space launcher under perturbation and atmospheric disturbance. By comparing the worst-case LTV analysis results with the results of corresponding nonlinear Monte Carlo simulations, the feasibility of the approach to provide necessary upper bounds is demonstrated. This comparison also highlights the improved computational speed of the proposed LTV approach compared to simulation-based nonlinear analyses