An Efficient Algorithm to Compute Norms for Finite Horizon, Linear Time-Varying Systems

We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both L2 and terminal Euclidean norm penalties on outputs. Existing computational approaches include power iteration bisection a Riccati Differential Equation (RDE). has low computation time per but overall convergence can be slow. In contrast, RDE condition provides guaranteed bounds gain single integration complementary features these two algorithms are combined develop new that is fast provable upper lower within desired tolerance. also worst-case disturbance input achieves bound norm. proof which shows for this problem converges monotonically. Finally, we show controllability Gramian based simpler method L 2 -to-Euclidean This used reachable set at any horizon. Numerical examples provided demonstrate proposed algorithm.