scholarly journals Robust Stabilization and Disturbance Rejection of Positive Systems with Time-Varying Delays and Actuator Saturation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xi Ding ◽  
Zhengrong Xiang ◽  
Chunyu Yang
Keyword(s):  
Disturbance Rejection ◽  
State Feedback ◽  
Actuator Saturation ◽  
Design Method ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Time Varying ◽  
Positive Systems ◽  
Closed Loop System

This paper focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. First, a convex hull representation is used to describe the saturation characteristics. By constructing an appropriate copositive type Lyapunov functional, we give sufficient conditions for the existence of a state feedback controller such that the closed-loop system is positive and asymptotically stable at the origin of the state space with a domain of attraction. Then, the disturbance rejection performance analysis in the presence of actuator saturation is developed viaL1-gain. The design method is also extended to investigate the problem ofL1-gain analysis for uncertain positive systems with time-varying delays and actuator saturation. Finally, three examples are provided to demonstrate the effectiveness of the proposed method.

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.

Fault-Tolerant Control for Linear Time-Variant Impulsive Singular Systems Subject to Actuator Saturation and L∞ Disturbances

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Mahmood Khatibi ◽  
Mohammad Haeri
Keyword(s):  
Control Problem ◽  
State Feedback ◽  
Actuator Saturation ◽  
Fault Tolerant ◽  
Linear Time ◽  
Singular Systems ◽  
Viscoelastic Model ◽  
Domain Of Attraction ◽  
Fault Tolerant Control ◽  
Time Varying

This paper explores the fault-tolerant control problem for uncertain impulsive singular linear time-variant (LTV) systems in the presence of bounded-power or L∞ disturbances. Here, a saturation avoidance mechanism is employed to prevent faulty actuators from overloading. Also, the conflict between attenuating the effect of L∞ disturbances and enlarging the domain of attraction is tackled by proposing a nonconstant state feedback controller. In addition, the proposed method is capable of tolerating time-varying faults. The suggested method is implemented on a mechanical viscoelastic model of cortical bone with impulsive and time-varying nature to evaluate its competency.

scholarly journals A Time-Varying Gain Design Method for State Feedback Control of Upper Triangular Nonlinear Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yanmin Yin
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Nonlinear Term ◽  
Design Method ◽  
State Feedback Control ◽  
Time Varying ◽  
Closed Loop System ◽  
Incremental Rate

In this paper, a time-varying gain design method is used to investigate the state feedback control problem of upper triangular nonlinear systems. Firstly, the nonlinear term recognizes an incremental rate relying on the unknown constant and the function with respect to time. Then, a time-varying gain design method is utilized to construct a state feedback controller. With the help of a suitable coordinate transformation and a Lyapunov function, one obtains that all the signals of the closed-loop system converge to zero. Finally, two numerical examples are presented to display the effectiveness of the time-varying gain design method.

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.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Event-triggered model predictive control of positive systems with random actuator saturation

2021 ◽  
Author(s):  
Junfeng Zhang ◽  
Suhuan Zhang ◽  
Peng Lin
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Actuator Saturation ◽  
Domain Of Attraction ◽  
Programming Approach ◽  
Interval Estimate ◽  
Positive Systems ◽  
Predictive Algorithm ◽  
Controller Gain ◽  
Event Triggered

Abstract This paper investigates the event-triggered model predictive control of positive systems with actuator saturation. Interval and polytopic uncertainties are imposed on the systems, respectively. First, a new model with actuator saturation obeying Bernoulli distribution is established, which is more general and powerful for describing the saturation phenomenon than the saturation in a certain way. Then, a linear event-triggering condition is constructed based on the state and error signal. An interval estimate approach is presented to reach the positivity and stability of the systems. The saturation part in the controller is technically transformed into a non-saturation part. Thus, a linear programming approach is proposed to compute the event-triggered controller gain and the corresponding domain of attraction gain. A predictive algorithm is introduced for the computation of the event-triggered controller parameters. Finally, an example is provided to illustrate the validity of the design.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

scholarly journals H∞Control for Flexible Spacecraft with Time-Varying Input Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ran Zhang ◽  
Tao Li ◽  
Lei Guo
Keyword(s):  
Design Method ◽  
Flexible Spacecraft ◽  
Input Delay ◽  
Control Input ◽  
Time Varying ◽  
Closed Loop System ◽  
Slack Variables ◽  
Attenuation Level ◽  
Delay Dependent ◽  
Dependent State

This paper is concerned withH∞control problem for flexible spacecraft with disturbance and time-varying control input delay. By constructing an augmented Lyapunov functional with slack variables, a new delay-dependent state feedback controller is obtained in terms of linear inequality matrix. These slack variables can make the design more flexible, and the resultant design also can guarantee the asymptotic stability andH∞attenuation level of closed-loop system. The effectiveness of the proposed design method is illustrated via a numerical example.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

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