Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

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 Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Songlin Wo ◽  
Xiaoxin Han
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient ◽  
Time Linear

The finite-time stability (FTS) problem of discrete-time linear singular systems (DTLSS) is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI) approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

scholarly journals Stability of Discrete Systems Controlled in the Presence of Intermittent Sensor Faults

2008 ◽  
Vol 2008 ◽  
pp. 1-11
Author(s):  
Rui Vilela Dionísio ◽  
João M. Lemos
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Sensor Faults ◽  
Closed Loop System ◽  
Reconstructed Signal ◽  
Time Invariant

This paper presents sufficient conditions for stability of unstable discrete time invariant models, stabilized by state feedback, when interrupted observations due to intermittent sensor faults occur. It is shown that the closed-loop system with feedback through a reconstructed signal, when, at least, one of the sensors is unavailable, remains stable, provided that the intervals of unavailability satisfy a certain time bound, even in the presence of state vanishing perturbations. The result is first proved for linear systems and then extended to a class of Hammerstein systems.

scholarly journals Anti-windup design with guaranteed regions of stability for discrete-time linear systems with saturating controls

2004 ◽  
Vol 15 (1) ◽  
pp. 3-9 ◽  
Author(s):  
João Manoel Gomes da Silva Jr. ◽  
Romeu Reginatto ◽  
Sophie Tarbouriech
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Basin Of Attraction ◽  
Loop System ◽  
Discrete Time System ◽  
Closed Loop System ◽  
Model Stability ◽  
Quadratic Lyapunov Functions ◽  
Time Linear

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system connected to a deadzone nonlinearity. From this model, stability conditions based on quadratic Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated stability region.

An LMI Approach to State Feedback H∞ Control for Switched Singular Linear Systems

2014 ◽  
Vol 875-877 ◽  
pp. 835-840
Author(s):  
Zhu Mu Fu ◽  
Bin Wang ◽  
Ai Yun Gao
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lmi Approach ◽  
Singular Linear Systems

In this paper, the problems of state feedback control for a class of switched singular linear systems are investigated. By constructing a novel switched Lyapunov functional and convex combinations techniques, a sufficient condition established in terms of strict linear matrix inequalities (LMIs) is presented such that the system is asymptotically stable and satisfies performance. An explicit expression for the state feedback stabilization sub-controller and switching rule are designed. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, in which the closed-loop system satisfies performance at each point in whole state-space through switching, although each sub-system doesn’t satisfy the performance and even is not asymptotically stable. A numerical example is provided to illustrate the validity of the proposed methods.

scholarly journals A Robust Fault-Tolerant Predictive Control for Discrete-Time Linear Systems Subject to Sensor and Actuator Faults

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2307
Author(s):  
Sofiane Bououden ◽  
Ilyes Boulkaibet ◽  
Mohammed Chadli ◽  
Abdelaziz Abboudi
Keyword(s):  
Model Predictive Control ◽  
Linear Systems ◽  
Predictive Control ◽  
Robust Stability ◽  
Discrete Time ◽  
Fault Tolerant ◽  
Linear Matrix ◽  
Input Constraints ◽  
Actuator Faults ◽  
Time Linear

In this paper, a robust fault-tolerant model predictive control (RFTPC) approach is proposed for discrete-time linear systems subject to sensor and actuator faults, disturbances, and input constraints. In this approach, a virtual observer is first considered to improve the observation accuracy as well as reduce fault effects on the system. Then, a real observer is established based on the proposed virtual observer, since the performance of virtual observers is limited due to the presence of unmeasurable information in the system. Based on the estimated information obtained by the observers, a robust fault-tolerant model predictive control is synthesized and used to control discrete-time systems subject to sensor and actuator faults, disturbances, and input constraints. Additionally, an optimized cost function is employed in the RFTPC design to guarantee robust stability as well as the rejection of bounded disturbances for the discrete-time system with sensor and actuator faults. Furthermore, a linear matrix inequality (LMI) approach is used to propose sufficient stability conditions that ensure and guarantee the robust stability of the whole closed-loop system composed of the states and the estimation error of the system dynamics. As a result, the entire control problem is formulated as an LMI problem, and the gains of both observer and robust fault-tolerant model predictive controller are obtained by solving the linear matrix inequalities (LMIs). Finally, the efficiency of the proposed RFTPC controller is tested by simulating a numerical example where the simulation results demonstrate the applicability of the proposed method in dealing with linear systems subject to faults in both actuators and sensors.

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 Stabilization of discrete-time LTI positive systems

2017 ◽  
Vol 27 (4) ◽  
pp. 575-594 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Linear Matrix ◽  
Positive System ◽  
Matrix Inequalities ◽  
Positive Systems ◽  
Feedback Controllers ◽  
Associated Solutions ◽  
State Observers ◽  
Time Linear

AbstractThe paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

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