scholarly journals H∞Control for Network-Based 2D Systems with Missing Measurements

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Bu Xuhui ◽  
Wang Hongqi ◽  
Zheng Zheng ◽  
Qian Wei
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
2D Systems ◽  
Matrix Inequalities ◽  
Stochastic Variable ◽  
Missing Measurements ◽  
Binary Distribution

The problem ofH∞control for network-based 2D systems with missing measurements is considered. A stochastic variable satisfying the Bernoulli random binary distribution is utilized to characterize the missing measurements. Our attention is focused on the design of a state feedback controller such that the closed-loop 2D stochastic system is mean-square asymptotic stability and has an  H∞disturbance attenuation performance. A sufficient condition is established by means of linear matrix inequalities (LMIs) technique, and formulas can be given for the control law design. The result is also extended to more general cases where the system matrices contain uncertain parameters. Numerical examples are also given to illustrate the effectiveness of proposed approach.

scholarly journals H∞ILC Design for Discrete Linear Systems with Packet Dropouts and Iteration-Varying Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Bu Xuhui ◽  
Zhang Hongwei ◽  
Song YunZhong ◽  
Yu Fashan
Keyword(s):  
Stochastic System ◽  
Networked Systems ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
Roesser Model ◽  
Stochastic Variable ◽  
Binary Distribution ◽  
Discrete Linear Systems ◽  
Intermittent Measurements

AnH∞iterative learning controller is designed for networked systems with intermittent measurements and iteration-varying disturbances. By modeling the measurement dropout as a stochastic variable satisfying the Bernoulli random binary distribution, the design can be transformed intoH∞control of a 2D stochastic system described by Roesser model. A sufficient condition for mean-square asymptotic stability andH∞disturbance attenuation performance for such 2D stochastic system is established by means of linear matrix inequality (LMI) technique, and formulas can be given for the control law design simultaneously. A numerical example is given to illustrate the effectiveness of the proposed results.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

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.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

scholarly journals New relaxed stability and stabilization conditions for both discrete and differential linear repetitive processes

2021 ◽  
Author(s):  
Marcin Boski ◽  
Robert Maniarski ◽  
Wojciech Paszke ◽  
Eric Rogers
Keyword(s):  
Iterative Learning Control ◽  
Experimental Validation ◽  
Linear Matrix ◽  
Control Law ◽  
2D Systems ◽  
Matrix Inequalities ◽  
Repetitive Processes ◽  
Numerical Examples ◽  
Linear Repetitive Processes ◽  
Stability And Stabilization

AbstractThe paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.

Disturbance Attenuation with Minimization of Ellipsoids Restricting Phase Trajectories in Transition and Steady State

2020 ◽  
Vol 21 (4) ◽  
pp. 195-199
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Steady State ◽  
Linear Matrix Inequalities ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequalities ◽  
Integral Control ◽  
Linear Dynamical Systems ◽  
Transition Mode ◽  
Phase Trajectories

Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state. 

scholarly journals An LMI Technique for the Global Stabilization of Nonlinear Polynomial Systems

2009 ◽  
Vol 4 (4) ◽  
pp. 348 ◽  
Author(s):  
Mohamed Moez Belhaouane ◽  
Riadh Mtar ◽  
Hela Belkhiria Ayadi ◽  
Naceur Benhadj Braiek
Keyword(s):  
State Feedback ◽  
Direct Method ◽  
Polynomial Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Global Stabilization ◽  
Matrix Inequalities ◽  
Global Asymptotic Stabilization ◽  
Stabilizing Control

This paper deals with the global asymptotic stabilization of nonlinear polynomial systems within the framework of Linear Matrix Inequalities (LMIs). By employing the well-known Lyapunov stability direct method and the Kronecker product properties, we develop a technique of designing a state feedback control law which stabilizes quadratically the studied systems. Our main goal is to derive sufficient LMI stabilization conditions which resolution yields a stabilizing control law of polynomial systems.

Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Li Yang ◽  
Xinzhi Liu ◽  
Zhigang Zhang
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Necessary And Sufficient

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

scholarly journals Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 217 ◽  
Author(s):  
Yuhong Huo ◽  
Jia-Bao Liu
Keyword(s):  
Time Delay ◽  
Stability Condition ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Matrix Inequalities

The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

Stabilization Conditions for a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Sunhua Huang ◽  
Bin Wang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Lyapunov Stability Theorem ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Closed Loop Systems

The stabilization problem of fractional-order nonlinear systems for 0<α<1 is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.

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