In this paper, a synchronization balancing control is proposed based on the contraction theory of stability for inverted pendulum.The control scheme is applied to balance an inverted pendulum mounted on a moving cart with two wheels.The equations of motion of the system are divided into two cascade systems using the control law partitioning method, which allows the designer to split the control design process into simpler parts for each isolated fragment not as lean still a marine shirt of the main system.Then two control laws are planned for the corresponding partitions.The main aim of the closed-loop system is to balance the pendulum and synchronize the transient behavior of the system state with a reference model 13th signal battalion with time-varying parameters.
The stability of method is guaranteed using the contraction theory, and the proposed control mechanism is investigated through the simulation study.The simulation result confirms the performance of the proposed controller and illustrate the feasibility of method.