Stability and performance analysis in the presence of LTV perturbations with bounded rates of variation: A Lyapunov based approach

Evaluating the stability and the performance properties of a system in the presence of time-varying parameters is often computationally demanding. A practical method is proposed in this paper to alleviate this computational cost. The stability conditions are first formulated as an LMI feasibility problem involving the search of a suitable parameter-dependent Lyapunov function. This problem is then solved for a finite number of parametric configurations and the validity of the resulting Lyapunov function is checked on the whole parametric domain using a μ-analysis based test. In case the validation fails, a worst-case configuration is determined using particle swarm optimization and the whole process is repeated using an augmented set of parametric configurations. The resulting iterative algorithm is successfully applied to a realistic fighter aircraft model.