ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms

The ℓ₂-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ₂-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.