Optimal switched law of switched linear systems based on convergence route

The performance and characteristics of a switched linear system would not be the same if the switching laws were different. An optimal switched law can greatly increase the capacity of a switched system. An approach was proposed to find the optimal switch law to create a convergent system. The proposed approach can make switched systems converge at the origin with the route being optimal. The process identified for designing the optimal switch law only depends on resolving matrix equations. A matrix equation is determined by the system matrices of the switched subsystems, so the determination and form of the equation is straightforward. Some sample simulations show that the proposed approach is simple and effective; and can be easily applied to real engineering problems.