Saturation-dependent Lyapunov Function Research Articles

Equivalent‐input‐disturbance‐based repetitive tracking control for Takagi–Sugeno fuzzy systems with saturating actuator

This study investigates the output tracking problem for a class of Takagi–Sugeno fuzzy systems subject to periodic signals and actuator saturation via equivalent-input-disturbance (EID) technique. In particular, to ensure the periodic signals tracking, a state-space repetitive control structure is considered. Further, the EID technique is utilised to improve the disturbance rejection performance without any prior knowledge of the disturbance and inverse dynamics of the plant. By constructing a suitable Lyapunov–Krasovskii functional and using the Wirtinger-based integral inequality, a new set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) which ensures the stability of the addressed system. In addition to that by using a Lyapunov level set, saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimisation problem. Moreover, the designed fuzzy repetitive controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation, but also in the presence of any actuator faults, saturation and dead zone. Finally, the proposed method is validated through two numerical examples to illustrate the effectiveness and superiority of the developed controller design.

Stability Analysis of Delta Operator Systems with Actuator Saturation by a Saturation-Dependent Lyapunov Function

This paper proposes the stability of delta operator systems subjected to actuator saturation by a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation in delta domain. Linear matrix inequalities-based methods are developed for analyzing the stability of the delta operator system. Numerical example is given to illustrate the effectiveness of the developed techniques.

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.

Stability analysis for continuous-time systems with actuator saturation

The aim of this paper is to study the determination of the stability regions for continuous-time systems subject to actuator saturation. Using an affine saturation-dependent Lyapunov function, a new method is proposed to obtain the estimation of the domain of attraction of the closed-loop system. A family of linear matrix inequalities (LMIs) that provides sufficient conditions for the existence of this type of Lyapunov function are presented. The results obtained in this paper can reduce the conservativeness compared with the existing ones. Numerical examples are given to illustrate the effectiveness of the proposed results.

STABILITY ANALYSIS AND ANTI-WINDUP DESIGN FOR DISCRETE-TIME SYSTEMS BY A SATURATION-DEPENDENT LYAPUNOV FUNCTION APPROACH

This paper deals with the stability analysis and anti-windup design of discrete-time systems subject to actuator saturation. We present a new saturation-dependent Lyapunov function to estimate the domain of attraction, which is then formulated and solved as a constrained LMI optimization problem. Further we propose an anti-windup compensation method to enlarge the domain of attraction in the presence of saturation. Numerical examples are presented to show the effectiveness of the proposed method.

Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed using a saturation-dependent Lyapunov function. This saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimization problem. Numerical examples are presented to show the effectiveness of the proposed method.