Li-Sheng Hu

Delay-dependent stochastic stability and H∞ analysis for time-delay systems with Markovian jumping parameters

Abstract This paper studies the problem of the stochastic stability and H∞ disturbance attenuation for linear continuous-time time-delay systems that possess randomly Markovian jumping parameters. A delay-dependent sufficient condition on the stochastic stability with given H∞ performance is proposed using the stochastic Lyapunov–Krasovskii stability theory. The conditions are formulated as a set of coupled linear matrix inequalities.

A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems

In this paper, we consider the H/sub 2/ sampled-data control for uncertain linear systems by the impulse response interpretation of the H/sub 2/ norm. Two H/sub 2/ measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H/sub 2/ criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.

A novel approach on stabilization for linear systems with time-varying input delay

Abstract This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method.

Multirate robust digital control for fuzzy systems with periodic Lyapunov function

Sampled-data control which is capable of stabilizing general nonlinear systems is of great current interest. In this paper, the Takagi-Sugeno (TS) fuzzy model is used to represent the nonlinear plant. The paper is primarily concerned with designing digital controllers for the TS fuzzy continuous-time model to stabilize the closed-loop system. In the problem formulation, we only assume that the sampled values at a sampling rate of (1/T/sub s/) are available for control. Within the sampling intervals, the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series. This digital control action is then fed into the nonlinear system through a zero-order-holder. In this paper, two kinds of digital controllers are designed: Multirate and single-rate digital controllers. Within a sampling interval, the single-rate controller is static, while the multirate controller is periodically time-varying, i.e., the control action is switched at a small switching period T. Clearly, for the single-rate case, this switching period T is equal to the sampling period T/sub s/. This paper presents a design procedure for the multirate fuzzy controller with the single-rate control as a special case. The results are formulated as linear matrix inequalities. Numerical example shows the effectiveness of the proposed design procedures.

Sampled-data control for time-delay systems

Abstract The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.

Robust digital model predictive control for linear uncertain systems with saturations

Actuator saturation constraint is inevitable in industrial process. In this paper, we consider a discrete receding horizon control, a piecewise constant robust model predictive control, for a continuous-time plant with actuator saturation constraint through a sampled-data control approach. The solution is formulated as an optimization problem subject to linear matrix inequalities. A numerical example is used to demonstrate the effectiveness of the proposed design procedure.

Stabilization of switched systems with time-varying delay: a state transformation method

In this paper, the problems of exponential stability and control design for switched systems with time-varying delay are investigated. Under a class of switching signals counting with average dwell time, a new less conservative stability condition is proposed for the systems. To facilitate controller design for the switched systems with time-varying input delay, a new state transformation method is developed, with which the non-linear term in matrix inequality is removed. The method is also applicable to the existing stability conditions for controller design, while the existing methods may be not able to obtain computational control procedures from the stability conditions. In this paper, the computational algorithms are established for the stability analysis and control synthesis. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Robust model predictive control for linear systems with constraints

The constraints make a process nonlinear even for a linear system in process control. A robust model predictive control (MPC) algorithm for the linear systems with disturbance by explicitly considering the constraints is proposed in this paper. By introducing an auxiliary system to the uncertain MPC system, the robust H2 problem is converted to an LQ problem. Then the constraint can be exploited explicitly. Based on polynomial matrix description of the plant, the robust MPC algorithm is formulated as an optimization problem of a semi-definite programming. The utility of the proposed algorithm is demonstrated through a numerical example.

Positive invariance of linear uncertain systems and applications

Sufficient and necessary conditions for nonlinear impulsive systems with respect to linear constraints with bounded additive disturbances are obtained from a characterization of positive invariance properties for these systems. As an application of results obtained, the sufficient conditions for discrete state feedback control and for asymptotic stabilization of linear uncertain systems with the state positively nonsymmetrical invariant set are presented. Furthermore, extensions to multirate sampled-data control are presented. Finally, a numerical example is given.

Robust sampled-data control for vehicle steering systems

In industrial control, computer control is widely used, which makes the closed-loop system be a sampled-data one containing continuous time and discrete time signals. In contrast to the traditional approximation methods, sampled-data synthesis is a direct digital controller design procedure without approximation. Sampled-data control which is capable of stabilizing general nonlinear systems with the intersample behavior taken into account are of great current interest. In the paper robust sampled-data control for a class of nonlinear parametric uncertain systems with constraints on the output imposed by time-domain performances is proposed. Based on the result of robust asymptotic stability of sampled-data systems with constraints on the state, robust sampled-data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated for vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by a proposed iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to show the result.