The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and it is affected by time-delay. A linear output feedback controller with a tunable scaling gain is constructed.By selecting an appropriate Lyapunov-Krasovskii functional the scaling gain can be adjusted to render the closed-loop system globally asymptotically stable.The results can also be extended to the non-triangular nonlinear time-delay systems. The proposed control law together with the observer is linear and memoryless in nature and therefore it is easy to implement in practice. Two computer simulations are conducted to illustrate the effectiveness of the proposed theoretical results.
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.
In order to design a suitable controller which can achieve accurate trajectory tracking and a good control performance, and guarantee the stability and robustness of a robot system due to external disturbances error and internal parameter variations, an adaptive switching control strategy is proposed. The proposed scheme is designed under the condition of bounded distances and consists of an adaptive switching law and a PD controller. Based on the Lyapunov stability theory, it is proved that the proposed scheme can guarantee the tracking performance of the robotic manipulator and is adapted to varying unknown loads. Simulations are carded out on a two-link robotic manipulator, which illustrate the feasibility and validity of the proposed control scheme and the robustness for variational payloads.
