Gao Huijun

Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems

Abstract The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function (PWQLF) is constructed and is used to obtain the stability conditions based on the linear matrix inequalities (LMIs).The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.

Compensation time-varying delays in networked control system via delay-dependent stabilization approach

The defining characteristic of a networked control system (NCS) is having a feedback loop that passes through a computer network. Contrasting to this time delay introduced by the network, a delay-dependent stabilization condition of discrete-time linear system with time-varying delays is proposed. Based on this condition, the stabilization controller and H/sub /spl infin// controller of NCS are constructed and the solutions of these controllers are given through an iterative procedure of a linear matrix inequality (LMI) minimum problem which is derived from cone complementarity linearization algorithm. A numerical example is given to illustrate the proposed results.

New approaches to robust l 2−l ∞ and H ∞ filtering for uncertain discrete-time systemsfiltering for uncertain discrete-time systems

The problems of robust l2−l∞ and H∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l2−l∞ or H∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.

Sliding mode H ∞ control for a class of uncertain nonlinear state-delayed systems

Abstract A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H ∞ control problem by designing a memoryless H ∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H ∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H ∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.

Model predictive control with missing data

This paper is concerned with the problem of robust model predictive control for discrete-time systems with packet losses. A stochastic process satisfying Bernoulli random binary distribution is utilized to model the packet losses, and a parameter dependent Lyapunov function is adopted to reduce the conservatism. The aim is to design a state feedback controller which minimizes an upper bound on a quadratic objective function at each sampling instant for all admissible packet losses and system parameter uncertainties, and the robust stochastic stability of the closed-loop system is guaranteed. The hard constraints on the variances of the inputs and outputs are also considered. All the conditions to solve the proposed problem are formulated in the framework of linear matrix inequalities (LMIs). A simulation example is given to illustrate the effectiveness of the proposed control methodology.

H ∞ filtering of 2-D systems with packet losses

This paper is concerned with the problem of robust Hinfin filtering for uncertain 2-D systems with intermittent measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurements transmission is assumed to be imperfect, which is modelled by a stochastic variable. Our attention is focused on the design of an Hinfin filter such that the filtering error system is stochastically stable and preserves a guaranteed Hinfin performance. This problem is solved in the parameter-dependent framework and the corresponding results are established in terms of LMIs. An example is provided to show the effectiveness of the proposed approach.

H ∞ filter design for quantum stochastic systems

This paper is concerned with the Hinfin filtering problem for a class of noncommutative linear stochastic systems, among which quantum technology has been well recognized to be a typical example. A new structure of slack variables is introduced to solve the Hinfin filtering problem which gives a sufficient condition for the existence of desired Hinfin filters for quantum systems in terms of linear matrix inequalities (LMIs). Two examples from quantum optics are given to show the effectiveness of the proposed approach.

Robust H ∞ filter design for 2DFM model

This paper is concerned with the robust H∞ filtering problem for uncertain two-dimensional (2-D) systems described by the Fornasini-Marchesini model. The polynomially parameter-dependent idea is first utilized to solve the robust H∞ filtering problem, with sufficient conditions for existence of the desired H∞ filters expressed in terms of linear matrix inequalities (LMIs). These conditions are developed based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. As the degree grows, test of increasing precision is obtained providing less conservative filter designs. An example is given to show the effectiveness of the proposed approach.