Time‐weighted MR for switched LPV systems via balanced realisation

A new model reduction (MR) method is developed for continuous‐time switched linear parameter‐varying (LPV) systems based on time‐weighted gramians. Using time‐weighted energy functionals and parameter‐independent multiple Lyapunov functions, the time‐weighted controllability and observability gramians are obtained. With a balanced transformation matrix optimally derived, the authors show that a balanced realisation can be achieved for the original switched LPV systems. A series of low‐order models for different weighting factors are yielded by state truncation or singular perturbation techniques. The reduced‐order models can preserve the stability. The feasibility and effectiveness of the proposed MR method are illustrated by two examples including a three spring‐mass system.