Time-varying stability analysis of linear systems with linear matrix inequalities

摘要

Aerospace attitude control systems are often modeled as time-varying linear systems. In industry, these systems are analyzed with linear time-invariant (LTI) methods by treating the system as slowly varying. Stability analysis with parameter dependent Lyapunov functions and linear matrix inequalities (LMIs) enables the consideration of bounds on system parameters' rates of variation while accounting for time-varying behavior. The LMI criteria are adapted to predict robustness in time-varying systems. In a case study, stability envelopes are created for time-varying uncertain parameters in a spacecraft. The time-of-flight is divided into intervals and analyzed using typical trajectories of time-varying parameters. For the uncertain parameter combinations considered, LMI stability criteria deduce that the system is stable and possesses stability margins that meet or exceed requirements for the time intervals that can be approximated by linear system models.