scholarly journals Performance Analysis for Discrete-Time Linear Systems with Saturated Linear Feedback: a Nonlinear Saturation-Dependent Gain-Scheduling Approach

2021 ◽  
Author(s):  
Nguyen Hoai Nam
Keyword(s):  
Performance Analysis ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Linear Matrix ◽  
Nonlinear Saturation ◽  
Feedback Matrix ◽  
Time Linear

In this paper, we propose a new technique for the performance analysis of discrete-time linear systems controlled by a saturated linear control law. Two performance indices, the computation of invariant sets and the L2 performance, are considered. The main contributions of the paper are the following: i) a new linear parameter varying system framework is presented to model the saturated system, ii) a nonlinear saturation-dependent auxiliary feedback matrix is considered, iii) new sufficient conditions for the performance analysis are proposed. It is shown that the conditions can be expressed as a set of linear matrix inequalities. Furthermore, it is shown that the conditions are guaranteed to be less conservative than existing solutions in the literature. Three numerical examples are presented to illustrate the effectiveness of the proposed method. <br>

scholarly journals Performance Analysis for Discrete-Time Linear Systems with Saturated Linear Feedback: a Nonlinear Saturation-Dependent Gain-Scheduling Approach

2021 ◽  
Author(s):  
Nguyen Hoai Nam
Keyword(s):  
Performance Analysis ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Linear Matrix ◽  
Nonlinear Saturation ◽  
Feedback Matrix ◽  
Time Linear

In this paper, we propose a new technique for the performance analysis of discrete-time linear systems controlled by a saturated linear control law. Two performance indices, the computation of invariant sets and the L2 performance, are considered. The main contributions of the paper are the following: i) a new linear parameter varying system framework is presented to model the saturated system, ii) a nonlinear saturation-dependent auxiliary feedback matrix is considered, iii) new sufficient conditions for the performance analysis are proposed. It is shown that the conditions can be expressed as a set of linear matrix inequalities. Furthermore, it is shown that the conditions are guaranteed to be less conservative than existing solutions in the literature. Three numerical examples are presented to illustrate the effectiveness of the proposed method. <br>

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.

scholarly journals Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition

2016 ◽  
Vol 26 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Performance Index ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.

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 Eigenvalue assignment in fractional descriptor discrete-time linear systems

2017 ◽  
Vol 27 (1) ◽  
pp. 119-128
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Necessary And Sufficient ◽  
Time Linear ◽  
Eigenvalue Assignment

Abstract The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.

Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs

2014 ◽  
Vol 62 (1) ◽  
pp. 85-89 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Necessary And Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Necessary and sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

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