A generating function approach to the input-to-state stability of discrete time switched linear systems
A switched linear system is a dynamical system consisting of a number of linear subsystems along with a switching rule that determines the switching among subsystems. Such systems exhibit rich dynamics despite their relatively simple structure. Stability analysis of switched linear systems has received a lot of attention in recent times. Current approaches to stability analysis include Lyapunov methods, Lie Algebraic methods and LMI methods. The present work focuses on characterizing the input-to-state stability of switched linear systems using a new concept of generating functions. To this end we propose a generalized notion of input-to-state ℓ 2-gains of discrete time controlled switched linear systems and proceed to develop the theory of generating functions. A generating function is an appropriately defined power series whose domain of convergence characterizes the generalized input-to-state ℓ2-gains of switched linear system. After suitable theoretical development we are able to study relevant properties of the generating functions and relate them to input-to-state stability of switched linear systems. Using dynamic programming, we also formulate an efficient numerical computation method that can be used to bound the input-to-state ℓ2-gains of switched linear systems.^
Jianghai Hu, Purdue University.
Applied Mathematics|Engineering, Electronics and Electrical