scholarly journals Stability of Interval Positive Fractional Discrete–Time Linear Systems

2018 ◽  
Vol 28 (3) ◽  
pp. 451-456 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Upper Bound ◽  
Asymptotically Stable ◽  
Kharitonov Theorem ◽  
Time Linear

Abstract The aim of this work is to show that interval positive fractional discrete-time linear systems are asymptotically stable if and only if the respective lower and upper bound systems are asymptotically stable. The classical Kharitonov theorem is extended to interval positive fractional linear systems.

scholarly journals Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems

2013 ◽  
Vol 62 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Electrical Circuit ◽  
Approximation Methods ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract The positive asymptotically stable continuous-time linear systems are approximated by corresponding asymptotically stable discrete-time linear systems. Two methods of the approximation are presented and the comparison of the methods is addressed. The considerations are illustrated by three numerical examples and an example of positive electrical circuit.

Positive and asymptotically stable realizations for descriptor discrete-time linear systems

2013 ◽  
Vol 61 (1) ◽  
pp. 229-237
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Asymptotically Stable ◽  
Transfer Matrices ◽  
Numerical Examples ◽  
Time Linear

Abstract Conditions for the existence of positive and asymptotically stable realizations for descriptor discrete-time linear systems are established. Procedures for computation of positive and asymptotically stable realizations for improper transfer matrices are proposed. The effectiveness of the methods is demonstrated on numerical examples

Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings

2013 ◽  
Vol 61 (2) ◽  
pp. 343-347 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Discrete Time System ◽  
Time System ◽  
Switched Linear Systems ◽  
Time Linear

Abstract The asymptotic stability of positive switched linear systems for any switchings is addressed. Simple sufficient conditions for the asymptotic stability of positive switched continuous-time and discrete-time linear systems are established. It is shown that the positive switched continuous-time (discrete-time) system is asymptotically stable for any switchings if the sum of entries of every column of the matrices of subsystems is negative (less than 1)

Inverse systems of linear systems

2010 ◽  
Vol 59 (3-4) ◽  
pp. 203-216 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Inverse System ◽  
Standard System ◽  
Asymptotically Stable ◽  
Inverse Systems ◽  
Time Linear

Inverse systems of linear systemsThe concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.

scholarly journals Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

2013 ◽  
Vol 23 (3) ◽  
pp. 501-506 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Stable ◽  
Type Approximation ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

Abstract Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

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.

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