Linna Zhou

Fast Sampling Control of Singularly Perturbed Systems with Actuator Saturation and Disturbance

We will consider the problem of fast sampling control for singularly perturbed systems subject to actuator saturation and disturbance. A sufficient condition for the existence of a state feedback controller is proposed. Under this controller, the boundedness of the trajectories in the presence of disturbances is guaranteed for any singular perturbation parameter less than or equal to a predefined upper bound. To improve the capacity of disturbance tolerance and disturbance rejection, two convex optimization problems are formulated. Finally, a numerical example is presented to demonstrate the effectiveness of the main results of this paper.

Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

Sampled-data H∞ filtering for Markovian jump singularly perturbed systems with time-varying delay and missing measurements

ABSTRACT In this paper, sampled-data H∞ filtering problem is considered for Markovian jump singularly perturbed systems with time-varying delay and missing measurements. The sampled-data system is represented by a time-delay system, and the missing measurement phenomenon is described by an independent Bernoulli random process. By constructing an ϵ-dependent stochastic Lyapunov–Krasovskii functional, delay-dependent sufficient conditions are derived such that the filter error system satisfies the prescribed H∞ performance for all possible missing measurements. Then, an H∞ filter design method is proposed in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the feasibility and advantages of the obtained results.

Anti-windup control for nonlinear singularly perturbed switched systems with actuator saturation

ABSTRACT This paper considers the problem of anti-windup (AW) control for nonlinear singularly perturbed switched systems with actuator saturation. An AW controller consisting of a dynamic state feedback (DSF) controller and an AW compensator is firstly constructed. Then, two methods are proposed to determine the AW controller gain matrices by a common Lyapunov function. One of which assumes that the singular perturbation parameter ϵ is available and designs ϵ-dependent AW controller gains simultaneously. The other one, which considers the case that ϵ is unknown but sufficiently small, designs the ϵ-independent DSF controller gain matrices first and then designs the ϵ-independent AW compensator gain matrices. Both of the methods are reduced to solving convex optimisation problems and can achieve larger stability bound and basin of attraction than the existing results. Finally, examples are used to illustrate the feasibility and advantages of the proposed methods.

Sampled-data control for singularly perturbed systems with actuator saturation

The issue of the sampled-data control for singularly perturbed systems (SPSs) with input saturation is considered. Based on the Lyapunov-Krasovskii functional and linear matrix inequality (LMI) approach, the design method of sampled-data controller for SPSs with actuator saturation is proposed. Then, the estimation of stability region is given by solving the convex optimization problem. Finally, numerical examples are provided to demonstrate the merits of the obtained results.

Control for T-S Fuzzy Singularly Perturbed Switched Systems

This paper is concerned with the design of fuzzy controller with guaranteed performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter is developed. This controller is shown to work well for all . Then, for sufficiently small an -independent controller design method is proposed. Furthermore, under the -independent controller, the -bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.

Controller design for T-S fuzzy singularly perturbed switched systems

This paper investigates the problem of fuzzy controller design for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. By using the average dwell time approach together with the piecewise Lyapunov function technique, a set of well-conditioned sufficient conditions for the existence of controller is proposed, under which the overall switched closed-loop system is asymptotically stable. A state feedback controller depending on the singular perturbation parameter ε, which is shown to work well for all ε ∈ (0, ε0), where ε0 is the stability bound of singularly perturbed systems, is developed. In addition, when ε is sufficiently small, the ε-dependent controller can be reduced to an ε-independent one. Then, an ε-independent state feedback stabilization controller design method is proposed in terms of linear matrix inequalities. Furthermore, under the controller, the stability bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to show the feasibility and effectiveness of the obtained results.

Control of singularly perturbed systems subject to actuator saturation

This paper considers the stabilization problem for singularly perturbed systems (SPSs) subject to actuator saturation. A state feedback stabilization controller design method is proposed and a basin of attraction is constructed. The proposed method is expressed in terms of linear matrix inequalities. The numerical problems due to the ill conditioning are avoided by using a non-decomposing strategy. Finally, two examples are given to show the advantages and effectiveness of the the method proposed in this paper.