Robust Stability Check of Fractional Discrete-Time Linear Systems with Interval Uncertainties

2015 ◽  
pp. 199-208 ◽  
Author(s):  
Mikołaj Busłowicz ◽  
Andrzej Ruszewski
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Interval Uncertainties ◽  
Time Linear

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.

Robust stability of positive discrete-time linear systems of fractional order

2010 ◽  
Vol 58 (4) ◽  
pp. 567-572 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Robust Stability ◽  
Discrete Time ◽  
Natural Order ◽  
Discrete Time System ◽  
Uncertainty Structure ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Robust stability of positive discrete-time linear systems of fractional orderThe paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order - in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order - in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order - in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.

Sparse Feedback Design in Discrete-Time Linear Systems

2018 ◽  
pp. 3-21
Author(s):  
Aleksey Bikov ◽  
◽  
Pavel Sherbakov ◽  
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Feedback Design ◽  
Time Linear
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