Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

Dynamical output feedback stabilization for neutral systems with mixed delays

This paper is concerned with the issue of stabilization for the linear neutral systems with mixed delays. The attention is focused on the design of output feedback controllers which guarantee the asymptotical stability of the closed-loop systems. Based on the model transformation of neutral type, the Lyapunov-Krasovskii functional method is employed to establish the delay-dependent stability criterion. Then, through the controller parameterization and some matrix transformation techniques, the desired parameters are determined under the delay-dependent design condition in terms of linear matrix inequalities (LMIs), and the desired controller is explicitly formulated. A numerical example is given to illustrate the effectiveness of the proposed method.

Output Feedback Stabilization of an Unstable Wave Equation with Observations Subject to Time Delay

This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.

Dynamic output feedback stabilization of deterministic finite automata via the semi-tensor product of matrices approach

This paper deals with the dynamic output feedback stabilization problem of deterministic finite automata(DFA).The static form of this problem is defined and solved in previous studies via a set of equivalent conditions.In this paper,the dynamic output feedback(DOF)stabilization of DFAs is defined in which the controller is supposed to be another DFA.The DFA controller will be designed to stabilize the equilibrium point of the main DFA through a set of proposed equivalent conditions.It has been proven that the design problem of DOF stabilization is more feasible than the static output feedback(SOF)stabilization.Three simulation examples are provided to illustrate the results of this paper in more details.The first example considers an instance DFA and develops SOF and DOF controllers for it.The example explains the concepts of the DOF controller and how it will be implemented in the closed-loop DFA.In the second example,a special DFA is provided in which the DOF stabilization is feasible,whereas the SOF stabilization is not.The final example compares the feasibility performance of the SOF and DOF stabilizations through applying them to one hundred random-generated DFAs.The results reveal the superiority of the DOF stabilization.