On positively invariant sets for discrete-time linear systems with disturbance: an application of maximal disturbance sets

1994 ◽  
Vol 39 (1) ◽  
pp. 245-249 ◽  
Author(s):  
E. De Santis
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Invariant Sets ◽  
Positively Invariant Sets ◽  
Time Linear

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.

Sign in / Sign up

Export Citation Format

Share Document