A Two-Norm Model of Linear Time-Varying System and Related Control Designs

In this thesis, we introduce a nonlinear state transformation to transform a linear time-varying system into a scalar system, which describes how the two-norm of the system state changes with the control input. With this two-norm scalar model, different control designs can be constructed, including the forward Riccati equation control, controllability grammian control, least-squares control, and the division control. However, even if the linear time-varying system is controllable, the two-norm
scalar system may lose its controllability in the process of control. Hence, further research is required in the future.