Hu, JianghaiShen, JinglaiPutta, Vamsi2024-08-272024-08-272016-01Hu, Jianghai, Jinglai Shen, and Vamsi Putta. “Generalized Input-to-State L2-Gains of Discrete-Time Switched Linear Control Systems.” SIAM Journal on Control and Optimization 54, no. 3 (January 2016): 1475–1503. https://doi.org/10.1137/15M1018046.https://doi.org/10.1137/15M1018046http://hdl.handle.net/11603/35856A generalized notion of input-to-state ℓ₂-gain is proposed for discrete-time switched linear control systems (SLCSs). Dependent on a discount factor of subsystem matrices, this generalized ℓ₂-gain provides new insight into input-to-state behaviors of the SLCSs under parameter variations. After establishing analytical properties of the generalized ℓ₂-gain, this paper focuses on the generating function approach to the study of the generalized ℓ₂-gain. Important properties of generating functions are derived, and it is shown that their radii of convergence characterize the generalized ℓ₂-gain. Furthermore, iterative algorithms are developed for computing the generating functions with proven uniform or exponential convergence. Numerical results show that these algorithms yield efficient estimates of both the generalized and classical ℓ₂-gains.29 pagesen-US© 2016, Society for Industrial and Applied Mathematics.Text