Using a canonical form transformation, original time-delay system is transformed into a delay-free system.
By using appropriate nonlinear state feedback and coordinate transformation method, a nonlinear system is transformed into a linear system partially or wholly, then the system controller can be designed based on the linear control method.
Then, with a state transformation, the closed-loop control system is transformed into a LTV form for which exponential stability can be guaranteed when a partial persistent excitation (PE) condition is satisfied.
First of all, it is shown that the unknown control coefficients are lumped together via a common coordinate transformation, thus the original switched nonlinear system is transformed into a new switched system for which control design is feasible.
First, the original system is transformed into a new defined system by a linear state transformation.
First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE ODE cascade with an invertible integral transformation, where PDE backstepping is employed.
First, based on a linear state transformation, the unknown control coefficients are lumped together and the original system is transformed to a new system for which control design becomes feasible.
First, through a linear state transformation, the unknown control coefficients are lumped together and the original system is transformed to a new system for which control design becomes feasible.
Thereafter, the physical system is transformed into a schematic diagram.
The system is transformed into two different subsystems.
Under some geometric conditions, the system is transformed into two different subsystems.
