Analysis and design for discrete-time singular systems with time-delay and actuator saturation by a saturation-dependent Lyapunov function

2016 ◽  
Author(s):  
Lei Fu ◽  
Yuechao Ma
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Singular Systems ◽  
Analysis And Design

scholarly journals Exponential Estimates and Stabilization of Discrete-Time Singular Time-Delay Systems Subject to Actuator Saturation

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Jinxing Lin
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Decay Rate ◽  
Discrete Time ◽  
Actuator Saturation ◽  
Singular Systems ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Exponential Estimates ◽  
Singular Time

This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

Stability and L2–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4197-4206 ◽  
Author(s):  
Jumei Wei ◽  
Huimin Zhi ◽  
Kai Liu
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Discrete Time ◽  
Text Analysis ◽  
Dwell Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Function Approach ◽  
Discrete Time Case

In this paper, the problem of the E-exponential stability and [Formula: see text] analysis of linear switched singular systems is investigated in discrete-time case. By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and [Formula: see text] analysis for linear switched singular systems are presented. Based on the above results, we also derive the weighted [Formula: see text] performance index. In addition, by utilizing our proposed method, tighter bounds on average dwell time can be obtained for our considered systems. At last, a numerical example is given to show the effectiveness of the results.

Robust stability for uncertain discrete singular systems with time-varying delays

2009 ◽  
Vol 223 (5) ◽  
pp. 713-720 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Robust Stability ◽  
Singular Systems ◽  
Time Varying ◽  
Numerical Example ◽  
Delay Bounds ◽  
Cross Terms ◽  
Discrete Singular Systems ◽  
Delay Dependent

This paper is concerned with the problem of delay-dependent robust stability for uncertain discrete singular systems with time-varying delays. Without introducing the free-weighting matrices to deal with the cross terms, a new and improved delay-dependent condition is established for the nominal systems to be regular, causal, and stable via a new Lyapunov function employing the integrated lower and upper time-delay bounds. The condition is also extended to the uncertain case. A numerical example is given to illustrate that the proposed methods are effective and lead to less conservatism than the existing ones.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

Design of an input amplitude-constrained discrete-time control system

1998 ◽  
Vol 212 (5) ◽  
pp. 339-344
Author(s):  
K Y Zhu ◽  
S M Krishnan
Keyword(s):  
Control System ◽  
Time Delay ◽  
Lyapunov Function ◽  
Discrete Time ◽  
System Model ◽  
Augmented System ◽  
Input Amplitude ◽  
Time Control ◽  
Regulation And Tracking ◽  
Stability Results

A discrete-time controller based on an augmented system is proposed. The controller globally stabilizes a class of type- m systems subject to an input amplitude constraint. It is shown that use of the augmented system model allows us to handle with ease the system with arbitrary zeros and especially time delay. Stability results for both regulation and tracking are established on the basis of Lyapunov function methods and simulations of the demonstration are also carried out.

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