scholarly journals A Parameter-Dependent Approach to Observer-BasedH∞Control for Networked Control LPV Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yanhui Li ◽  
Xiujie Zhou ◽  
Chang Zhang ◽  
Hamid Reza Karimi
Keyword(s):  
Collaborative Design ◽  
Controller Design ◽  
Lyapunov Stability Theory ◽  
Networked Control ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Time Varying ◽  
Infinite Dimensional ◽  
Lpv Systems ◽  
Parameter Dependent

We address the observer-basedH∞controller design problem for networked control LPV (NC LPV) systems, which are network-based systems that depend on unknown but measurable time-varying parameters. According to the analysis of the special issues brought by introducing network into LPV systems and the state reconstruction based on the observer, a new augmented model is established with two independent time-varying delays, which can carry out the controller and observer collaborative design effectively. Based on the parameter-dependent Lyapunov stability theory, a sufficient condition is proposed to ensure that the closed-loop system is asymptotically stable with a guaranteedH∞performance levelγ, in which the coupling between Lyapunov function matrices and the system matrices existed. By using the Projection Lemma and introducing a slack matrix, the decoupling is achieved successfully, which refers to reducing conservatism. In the present study, the condition for stability analysis and control synthesis is formulated in terms of the parameterized linear matrix inequality (PLMI), which is infinite-dimensional and can be transformed into finite by using the basis function method and gridding technique. A numerical example is given to demonstrate the high validity and merit of the proposed approach.

scholarly journals An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
P. Bumroongsri
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Control Laws ◽  
Lpv Systems ◽  
Parameter Dependent ◽  
Dependent State

An offline model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

α-Stabilization Criterion for Networked Control Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1858-1862 ◽  
Author(s):  
Li Sheng Wei ◽  
Zhi Hui Mei ◽  
Ming Jiang
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Optimization Problem ◽  
Networked Control Systems ◽  
Lyapunov Stability Theory ◽  
Networked Control ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Lmi Approach ◽  
Network Transmission

This study focus on α-Stability constraints for uncertain networked control systems (NCSs) subject to disturbance inputs, where the network transmission is connected with time-delay and packet dropout. The overall NCSs model is derived. In order to obtain much less conservative results, the sufficient condition for feasibility is presented in term of 2nd Lyapunov stability theory and a set of linear matrix inequalities (LMIs). This LMI approach can be the optimization problem of computation of the maximal allowed bound on the time-delay for NCSs.

scholarly journals Resilient Robust Finite-TimeL2-L∞Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Controller Design ◽  
Linear Matrix ◽  
Neutral System ◽  
Time Varying ◽  
Constraint Condition ◽  
Closed Loop System ◽  
Delayed System ◽  
Delay Dependent

The delay-dependent resilient robust finite-timeL2-L∞control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a givenL2-L∞constraint condition. Simulation results illustrate the validity of the proposed approach.

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.

scholarly journals Anti-Saturation Control of Uncertain Time-Delay Systems with Actuator Saturation Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 375
Author(s):  
Hejun Yao
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Saturation Control ◽  
Systems Model

The problem of anti-saturation control for a class of time-delay systems with actuator saturation is considered in this paper. By introducing appropriate variable substitution, a new delay time-delay systems model with actuator saturation systems is established. Based on the Lyapunov stability theory, the stability condition and the anti-saturation controller design method are obtained by using the linear matrix inequality approach. By introducing the matrix into the Lyapunov function, the proposed conditions are less conservative than the previous results. Finally, a simulation example shows the validity and rationality of the method.

scholarly journals Output feedback controller design for polynomial linear parameter varying system via parameter-dependent Lyapunov functions

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769032 ◽  
Author(s):  
Xiaobao Han ◽  
Zhenbao Liu ◽  
Huacong Li ◽  
Xianwei Liu
Keyword(s):  
Output Feedback ◽  
Optimization Problem ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Output Feedback Controller ◽  
Parameter Varying ◽  
Parameter Dependent

This article presents a new output feedback controller design method for polynomial linear parameter varying model with bounded parameter variation rate. Based on parameter-dependent Lyapunov function, the polynomial linear parameter varying system controller design is formulated into an optimization problem constrained by parameterized linear matrix inequalities. To solve this problem, first, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameter-dependent Lyapunov function, controller, and object coefficient matrices. Then, the control solving problem was reduced to a normal convex optimization problem with linear matrix inequalities constraint on a newly constructed convex polyhedron. Moreover, a parameter scheduling output feedback controller was achieved on the operating condition, which satisfies robust performance and dynamic performances. Finally, the feasibility and validity of the controller analysis and synthesis method are verified by the numerical simulation.

scholarly journals Robust Gain–Scheduled PID Controller Design For Uncertain LPV Systems

2015 ◽  
Vol 66 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Vojtech Veselý ◽  
Adrian Ilka
Keyword(s):  
Pid Controller ◽  
Controller Design ◽  
Design Procedure ◽  
Quadratic Stability ◽  
Performance Quality ◽  
Lpv Systems ◽  
Guaranteed Cost ◽  
Pid Controller Design ◽  
Parameter Dependent ◽  
Gain Scheduled

Abstract A novel methodology is proposed for robust gain-scheduled PID controller design for uncertain LPV systems. The proposed design procedure is based on the parameter-dependent quadratic stability approach. A new uncertain LPV system model has been introduced in this paper. To access the performance quality the approach of a parameter varying guaranteed cost is used which allowed to reach for different working points desired performance. Numerical examples show the benefit of the proposed method.

ROBUST H∞ FILTERING FOR A CLASS OF NONLINEAR UNCERTAIN SINGULAR SYSTEMS WITH TIME-VARYING DELAY

2013 ◽  
Vol 11 (05) ◽  
pp. 1350035 ◽  
Author(s):  
JIQING QIU ◽  
ZIRUI XING ◽  
LI LI ◽  
MOHAN YANG ◽  
YI LI
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Singular Systems ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Satisfy Lipschitz Condition ◽  
Uncertain Singular Systems ◽  
Varying Delay

This paper focuses on the problem of robust H∞ filtering for a class of nonlinear uncertain singular systems with time-varying delay. First of all, the definition of robust H∞ filter is given. Considering the nonlinear disturbance link to uncertain singular systems with time-varying delay effects, the design idea of full-order robust H∞ filter based on the Lyapunov stability theory is presented. Under the condition that nonlinear uncertain functions satisfy Lipschitz condition, the sufficient condition under which nonlinear uncertain delayed filtering error singular systems are asymptotically stable and satisfy the robust H∞ performance is obtained by Lyapunov stability theory and linear matrix inequality (LMI) methods. Finally, two numerical examples are given to show the applicability of the proposed method.

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