Robust Stabilization and Disturbance Rejection for a Class of Hybrid Linear Systems Subject to Exponential Uncertainty

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Fei Long ◽  
Changlin Li ◽  
Changzheng Cui ◽  
Shumin Fei
Keyword(s):  
Linear Systems ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Robust Stabilization ◽  
Convex Polytope ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Taylor Series Approximation ◽  
Model Subject

In this paper, we address the problem of robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainties. By using Taylor series approximation and convex polytope technique, the exponentially uncertain hybrid linear system is transformed into an equivalent hybrid polytopic model subject to norm bounded uncertainty. For such equivalent hybrid linear model, we design its switching strategy and associated state feedback controllers so that such model is asymptotically stable with H∞ disturbance attenuation based on multiple Lyapunov function technology and linear matrix inequality (LMI) approach.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

scholarly journals A Switched Approach to Robust Stabilization of Multiple Coupled Networked Control Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Mei Yu ◽  
Nan Ding ◽  
Wen Tan ◽  
Junyan Yu
Keyword(s):  
Control Systems ◽  
State Feedback ◽  
Communication Channel ◽  
Networked Control Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Feedback Controllers ◽  
Limited Communication ◽  
Controlled Systems

This paper proposes a switched approach to robust stabilization of a collection of coupled networked controlled systems (NCSs) with node devices acting over a limited communication channel. We suppose that the state information of every subsystem is split into different packets and only one packet of the subsystem can be transmitted at a time. Multiple NCSs with norm-bounded parameter uncertainties and multiple transmissions are modeled as a periodic switched system in this paper. State feedback controllers can be constructed in terms of linear matrix inequalities. A numerical example is given to show that a collection of uncertain NCSs with the problem of limited communication can be effectively stabilized via the designed controller.

scholarly journals Event-Triggered Output-Feedback Control for Disturbed Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hao Jiang ◽  
Cui Zhang
Keyword(s):  
Linear Systems ◽  
Resource Utilization ◽  
Output Feedback ◽  
State Feedback ◽  
Output Feedback Control ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Disturbed Systems ◽  
Event Triggered

In the last few decades, event-triggered control received considerable attention, because of advantages in reducing the resource utilization, such as communication load and processor. In this paper, we propose an event-triggered output-feedback controller for disturbed linear systems, in order to achieve both better resource utilization and disturbance attenuation properties at the same time. Based on our prior work on state-feedback H∞ control for disturbed systems, we propose an approach to design an output-feedback H∞ controller for the system whose states are not completely observable, and a sufficient condition guaranteeing the asymptotic stability and robustness of the system is given in the form of LMIs (Linear Matrix Inequalities).

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

scholarly journals Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Chekib Ghorbel ◽  
Amira Tiga ◽  
Naceur Benhadj Braiek
Keyword(s):  
Tracking Control ◽  
Robust Stabilization ◽  
Fuzzy Model ◽  
Nonlinear Dynamic System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
S Model

This paper presents a proportional parallel distributed compensation (PPDC) design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed Takagi–Sugeno (T-S) fuzzy model. The proposed PPDC control design can greatly reduce the number of adjustable parameters involved in the original PDC and separate them from the feedback gain. Furthermore, the process of finding the common quadratic Lyapunov matrix is simplified. Then, the global asymptotic stability with decay rate and disturbance attenuation of the closed-loop T-S model affected by uncertainties and external disturbances are discussed using the H∞ synthesis and linear matrix inequality (LMI) tools. Finally, to illustrate the merit of our purpose, numerical simulation studies of stabilizing and tracking an inverted pendulum system are presented.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

Robust Reliable Sliding Mode H∞ Control for Uncertain Stochastic Nonlinear Jump Systems with Actuator Failures

2011 ◽  
Vol 480-481 ◽  
pp. 1475-1479
Author(s):  
Zhong Yi Tang ◽  
Sang Chen Ni ◽  
Wei Ping Duan
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Sliding Mode ◽  
Uncertain System ◽  
The State ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Sliding Surface ◽  
State Matrix ◽  
Actuator Failures

The problems of stochastic stability and robust reliable sliding mode H∞ control for a class of nonlinear matched and mismatched uncertain systems with stochastic jumps are considered in this paper. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix. The transition of the jumping parameters in the systems is governed by a finite-state markov process. A sufficient condition is given for the existence of integral sliding surface in terms of linear matrix inequalities (LMIs). Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. Moreover, a state feedback controller is also constructed by using the solution of LMIS. Finally, we give a design example in order to show the effectiveness of our method.

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