The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.
To improve the dynamic characteristics and the coupling capability, a new predictive functional control algorithm is proposed for strong coupling multivariable systems with time delay, which combines predictive functional control and decoupliug control. First, a decoupling control algorithm is proposed, in which first-order models with time delay are established by analyzing the amplitude-frequency and phase-frequency characteristics of the decoupled subject. Then, a controller is designed for the single-variable subjects after decoupling based on the principles of predictive functional control. The simulation results show that this proposed algorithm has less online computation time and faster tracking. It can provide a more effective control for complex multivariable systems.
