scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

scholarly journals Optimal guaranteed cost filtering for Markovian jump discrete-time systems

2004 ◽  
Vol 2004 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Peng Shi
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
State Estimator ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Discrete Time Systems ◽  
Linear State ◽  
Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Yong-Hong Lan ◽  
Jun-Jun Xia ◽  
Yue-Xiang Shi
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

Delay-dependent stability criterion for uncertain discrete time systems in presence of actuator saturation

2017 ◽  
Vol 40 (6) ◽  
pp. 1873-1891 ◽  
Author(s):  
Vipin Chandra Pal ◽  
Richa Negi
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
External Disturbance ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Time Systems

In this paper, the idea of triple Lyapunov functional is applied for controller design of discrete time systems subjected to various nonlinearities like actuator saturation, time varying delay and uncertainties. The performance of the system considered has been examined using H∞ technique in presence of external disturbance. A novel augmented triple Lyapunov-Krasovskii functional is applied with reciprocal convex approach to achieve the stability conditions, which are based on Linear Matrix Inequality. Saturation nonlinearity is tackled using less conservative convex hull method. Numerical examples are provided to illustrate the effectiveness of the proposed criterion.

scholarly journals Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

2018 ◽  
Author(s):  
Yong-Hong Lan ◽  
Xia Jun-Jun
Keyword(s):  
Dynamic System ◽  
Control Problem ◽  
Discrete Time ◽  
Repetitive Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems ◽  
Repetitive Controller

A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.

scholarly journals Delay-Partitioning Approach to Stability of Linear Discrete-Time Systems with Interval-Like Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Priyanka Kokil ◽  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This paper is concerned with the problem of global asymptotic stability of linear discrete-time systems with interval-like time-varying delay in the state. By utilizing the concept of delay partitioning, a new linear-matrix-inequality-(LMI-) based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion does not involve any free weighting matrices but depends on both the size of delay and partition size. The developed approach is extended to address the problem of global asymptotic stability of state-delayed discrete-time systems with norm-bounded uncertainties. The proposed results are compared with several existing results.

scholarly journals Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

2020 ◽  
Vol 48 (4) ◽  
pp. 633-659
Author(s):  
Daniel Bankmann ◽  
Volker Mehrmann ◽  
Yurii Nesterov ◽  
Paul Van Dooren
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Convex Set ◽  
Solution Set ◽  
Linear Matrix ◽  
Analytic Center ◽  
Matrix Equations ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Time Systems

AbstractIn this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

scholarly journals New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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