Robust State-Feedback Controller Design for Uncertainty Singular Systems

2011 ◽  
Vol 383-390 ◽  
pp. 32-37
Author(s):  
Li Ming Liang ◽  
Fa Lu Weng ◽  
Yuan Chun Ding
Keyword(s):  
Controller Design ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Robust Controller ◽  
Uncertain Singular Systems ◽  
Stability And Stabilization ◽  
The Stability ◽  
Parameter Dependent ◽  
Robust Stability And Stabilization

In this paper the problem of robust stability and stabilization of a class of uncertain singular Systems with uncertainties in both the derivative and state matrices is studied. By using a parameter dependent Lyapunov function, we derive the linear matrix inequalities (LMIs) based sufficient conditions for the stability and stabilization of the system. By solving these LMIs, the robust controller is derived. Finally, the numerical example is given to show the effectiveness of the proposed theorems.

Robust PD State Feedback Controller Design for Uncertain Singular Systems

2011 ◽  
Vol 403-408 ◽  
pp. 3813-3818
Author(s):  
Jian Wu Zhu ◽  
Yuan Chun Ding
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Closed Loop Systems ◽  
Uncertain Singular Systems ◽  
Parameter Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problem of robust stability and stabilization of singular systems with uncertainties in both the derivative and state matrices. By using a parameter dependent Lyapunov function, we derive the LMI-based sufficient conditions for the stabilization of the singular systems. Secondly, by solving these LMIs, a proportional plus derivative (PD) state feedback controller is designed for the closed-loop systems to be quadratically normal and quadratically stable (QNQS). Finally, the numerical example is given to show the effectiveness of the proposed theorems.

scholarly journals Stability and Stabilization of Continuous-Time Markovian Jump Singular Systems with Partly Known Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jumei Wei ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Controller Design ◽  
Partial Information ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
The Stability

This paper investigates the problem of the stability and stabilization of continuous-time Markovian jump singular systems with partial information on transition probabilities. A new stability criterion which is necessary and sufficient is obtained for these systems. Furthermore, sufficient conditions for the state feedback controller design are derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

Robust Stabilization of Stochastic Singular Systems with Markovian Switching

2012 ◽  
Vol 591-593 ◽  
pp. 1496-1501
Author(s):  
Yu Cai Ding ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Markovian Jump Parameters ◽  
Stochastic Disturbance ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

In this paper, robust stability and stabilization of singular stochastic hybrid systems are investigated. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbance, Markovian jump parameters as well as time-varying delays. The aim of this paper is to design a state controller such that the dynamic system is robust stable. By using the Lyapunov-Krasovskii functional and Itô's differential rule, delay-range-dependent sufficient conditions on robust stability and stabilization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.

Robust H∞ Control for a Class of Nonlinear Uncertain Singular Systems with Time Delays both in State and Output

2013 ◽  
Vol 760-762 ◽  
pp. 1126-1130
Author(s):  
Jun Kang Hao ◽  
Guo Gang Li ◽  
Lian Qing Su
Keyword(s):  
Time Delays ◽  
Controller Design ◽  
Singular Systems ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Robust Performance ◽  
Robust Controller ◽  
Uncertain Singular Systems ◽  
Design Idea ◽  
Robust Controller Design

This paper discusses the problem of robust control for a class of nonlinear uncertain singular systems with time delays. Considering the nonlinear disturbance link to uncertain singular systems with time delays effects, the design idea of robust controller is presented. Using Lyapunov stability theory and linear matrix inequality (LMI) method, a robust controller design example of such nonlinear uncertain singular systems with time delays both in state and output is given. Under nonlinear uncertain functions satisfying Lipschitz condition, a sufficient condition of such nonlinear uncertain singular systems which are asymptotically stable and satisfy the robust performance is obtained. Finally, a numerical example is given to show the applicability of the proposed method.

scholarly journals Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α<2Case

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yuanhua Li ◽  
Heng Liu ◽  
Hongxing Wang
Keyword(s):  
Fractional Order ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Interval System ◽  
Interval Coefficients ◽  
Stability And Stabilization ◽  
Necessary And Sufficient ◽  
Robust Stability And Stabilization

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

scholarly journals Krasovskii Passivity and μ-Synthesis Controller Design for Quasi-Linear Affine Systems

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5571
Author(s):  
Vlad Mihaly ◽  
Mircea Şuşcă ◽  
Petru Dobra
Keyword(s):  
Path Planning ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Robust Controller ◽  
Affine Nonlinear Systems ◽  
Linearized System

This paper presents an end-to-end method to design passivity-based controllers (PBC) for a class of input-affine nonlinear systems, named quasi-linear affine. The approach is developed using Krasovskii’s method to design a Lyapunov function for studying the asymptotic stability, and a sufficient condition to construct a storage function is given, along with a supply-rate function. The linear fractional transformation interconnection between the nonlinear system and the Krasovskii PBC (K-PBC) results in a system which manages to follow the provided input trajectory. However, given that the input and output of the closed-loop system do not have the same physical significance, a path planning is mandatory. For the path planning component, we propose a robust controller designed using the μ-synthesis mixed-sensitivity loop-shaping for the linearized system around a desired equilibrium point. As a case study, we present the proposed methodology for DC-DC converters in a unified manner, giving sufficient conditions for such systems to be Krasovskii passive in terms of Linear Matrix Inequalities (LMIs), along with the possibility to compute both the K-PBC and robust controller alike.

scholarly journals Synchronization and Control of Linearly Coupled Singular Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fang Qingxiang ◽  
Peng Jigen ◽  
Cao Feilong
Keyword(s):  
Singular Systems ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Coupling Matrix ◽  
The Stability ◽  
And Control

The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI), indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.

scholarly journals A Robust Formation Control Strategy for Multi-Agent Systems with Uncertainties via Adaptive Gain Robust Controllers

2021 ◽  
Vol 11 (2) ◽  
pp. 71-87
Author(s):  
Shun Ito ◽  
Kaoru Ohara ◽  
Yoshikatsu Hoshi ◽  
Hidetoshi Oya ◽  
Shunya Nagai
Keyword(s):  
Formation Control ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Multi Agent System ◽  
Matrix Inequalities ◽  
Multi Agent Systems ◽  
Robust Controller ◽  
Multi Agent

This paper deals with a design problem of an adaptive gain robust controller which achieves consensus for multi-agent system (MAS) with uncertainties. In the proposed controller design approach, the relative position between the leader and followers are considered explicitly, and the proposed adaptive gain robust controller consisting of fixed gains and variable ones tuned by time-varying adjustable parameters can reduce the effect of uncertainties. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are reduced to solvability of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust formation control system is verified by simple numerical simulations. A main result of this study is that the proposed adaptive gain robust controller can achieve consensus and formation control giving consideration to relative distance in spite of uncertainties.

scholarly journals Reliablel2–l∞andH∞Control for Nonlinear Singular Systems via Dynamic Output Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lin Li ◽  
Yuting Kang
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Nonlinear Controller ◽  
Dynamic Feedback Control ◽  
Disturbance Attenuation Level

The reliablel2–l∞andH∞control for a class of Lipschitz nonlinear discrete-time singular systems with time delay is investigated via dynamic feedback control. The main goal of this paper is to design a generalized nonlinear controller such that, for possible actuator failures, the closed-loop system is regular, casual, and stable with a givenl2–l∞andH∞disturbance attenuation level being satisfied. Some sufficient conditions are obtained in terms of linear matrix inequalities (LMIs), and the controller design method is also proposed. Finally, a numerical example is included to illustrate the effectiveness of our proposed results.

scholarly journals Robust Stability and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinxing Lin ◽  
Lina Rong
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Delay Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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