Lin Chai

Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient conditions are derived in terms of linear operator inequalities framework for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these linear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the systems parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.

Global stabilisation for a class of uncertain nonlinear time-delay systems by dynamic state and output feedback

This paper investigates the design problem of constructing the state and output feedback stabilisation controller for a class of uncertain nonlinear systems subject to time-delay. First, a dynamic linear state feedback control law with an adaptive strategy is developed to globally stabilise the uncertain nonlinear time-delay system under a lower-triangular higher-order growth condition. Then, one more challenging problem of the adaptive output feedback stabilisation is addressed, which can globally stabilise the time-delay system when the unmeasurable states linearly grow with rate functions consisting of higher-order output.

Global Output Control for a Class of Inherently Higher-Order Nonlinear Time-Delay Systems Based on Homogeneous Domination Approach

This paper addresses the problem of global output feedback stabilization for a class of inherently higher-order uncertain nonlinear systems subject to time-delay. By using the homogeneous domination approach, we construct a homogeneous output feedback controller with an adjustable scaling gain. With the aid of a homogeneous Lyapunov-Krasovskii functional, the scaling gain is adjusted to dominate the time-delay nonlinearities bounded by homogeneous growth conditions and render the closed-loop system globally asymptotically stable. In addition, we also show that the proposed approach is applicable for time-delay systems under nontriangular growth conditions.

An Improved Approach of Adaptive Control for Time-Delay Systems Based on Observer

This paper is concerned with the problem of observer-based stabilization for time-delay systems. Both the state delay and input delay under consideration are assumed to be a constant time-delays, but not known exactly. A new design method is proposed for an observer-based controller with adaptation to the time-delays. The designed controller simultaneously contains both the current state and the past information of systems. The design for adaptation law to delay constants is more concise than the existing conclusions. The controller can be derived by solving a set of linear matrix inequalities (LMIs).

Global output feedback stabilization for a class of nonlinear time-delay systems via linear sampled-data control

This thesis researches the problem of global stabilization via output feedback by using linear sampled data controller for a family of nonlinear time-delay systems which satisfy a linear growth condition. Firstly, an inductive approach is proposed to estimate the state growth in nonlinear time-delay systems. Secondly, in the condition of just the output is measurable, a linear sampled data controller via output feedback with a scaling gain is designed by means of output domination method. Finally, the scaling gain which is a positive constant and a appropriate sampling period are determined to stabilize the closed-loop system asymptotically.

Semi-Global Stabilization via Homogeneous Output Feedback for a Class of Nonlinear Time-Delay Systems

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous domination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the scaling gain is adjusted such that the closed-loop system is semi-global asymptotically stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

Stabilization control for a class of complicated distributed time-delay systems with adaptation regard to delay parameter

This paper addresses the problem on stabilization for a class of complicated distributed time-delay systems. The distributed form is bounded with a time-varying function, and the distributed time-delay under consideration is assumed to be a constant time-delay, but not known precisely. A stabilization method is proposed for a dynamic memory Proportional and Integral (PI) feedback controller with adaptation to distributed time-delay. The controller can be derived by solving a set of dynamic linear matrix inequalities (LMIs).

Finite-time stabilization of fractional-order systems with model uncertainties and external disturbances

In this paper, a fractional-order sliding mode controller is proposed to realize the finite-time stabilization of fractional order (FO) system. The FO systems are perturbed by model uncertainties and external disturbances. First, a new fractional non-singular terminal sliding surface with desired dynamics is proposed. Subsequently, on the basis of Lyapunov function and finite-time control theory, a robust control law is introduced to guarantee the occurrence of the sliding motion in a given time. It demonstrates that reaching and sliding phases both are finite-time convergent. Finally, an example is provided to illustrate the effectiveness of the proposed method.

State feedback stabilization for a class of nonlinear time-delay systems via dynamic linear controllers

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.

Memory State-Feedback Stabilization for a Class of Time-Delay Systems with a Type of Adaptive Strategy

Stabilization of a class of systems with time delay is studied using adaptive control. With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed. The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality (LMI) design approach. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.