Generalized dynamic observer design for quasi-LPV systems

2018 ◽  
Vol 66 (3) ◽  
pp. 225-233 ◽  
Author(s):  
A.-J. Pérez-Estrada ◽  
G.-L. Osorio-Gordillo ◽  
M. Darouach ◽  
V.-H. Olivares-Peregrino
Keyword(s):  
Linear Matrix Inequalities ◽  
Estimation Error ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Algebraic Constraints ◽  
Dynamic Observer

Abstract This paper presents a new generalized dynamic observer (GDO) for quasi-linear parameter varying (LPV) systems. It generalises the structures of the proportional observer (PO) and proportional integral observer (PIO). The design of the GDO is derived from the solution of linear matrix inequalities (LMIs) and the solution of the algebraic constraints obtained from the estimation error analysis. The efficiency of the proposed approach is illustrated by a numerical example.

Control of LPV systems subject to state constraints and input saturation

2018 ◽  
Vol 40 (14) ◽  
pp. 3985-3993 ◽  
Author(s):  
Yanmei Hu ◽  
Guangren Duan ◽  
Feng Tan
Keyword(s):  
Linear Matrix Inequalities ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Parameter Uncertainties ◽  
Linear Parameter Varying ◽  
Linear Parameter Varying Systems ◽  
Parameter Varying

This paper deals with the stabilization of state-constrained linear parameter-varying systems subject to parameter uncertainties and input saturation. Based on a class of parameter-dependent Lyapunov functions, and the set invariance, sufficient conditions for the stabilization problem of the linear parameter-varying systems are established in terms of parameterized linear matrix inequalities. Further, these conditions are converted into linear matrix inequalities by using a parameter relaxation technique. Finally, detailed simulation results are presented to illustrate the effectiveness of the proposed methodology.

An observer-based H∞ linear parameter varying controller for time delayed linear parameter varying systems using dilated linear matrix inequalities and Wirtinger inequality

2021 ◽  
pp. 014233122098362
Author(s):  
Mohamed Hechmi Bouazizi
Keyword(s):  
Linear Matrix Inequalities ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Synthesis Conditions ◽  
Time Varying Delay ◽  
Parameter Varying

In this study, we give a method for the design of linear parameter varying (LPV) observers in order to perform an LPV time delayed state feedback control for LPV systems with time varying delay. We derive some tractable analysis and synthesis conditions expressed in terms of linear matrix inequalities (LMIs). We show how it is possible to reduce significantly the conservatism of the quadratic approach by using parameter dependent Lyapunov-Krasovskii functional and LMI dilation techniques jointed to the Wirtinger integral inequality. We also present a method that makes it possible to do without the separation principle when determining the observer and the state feedback parameters. The synthesis problem is formulated without this principle. A numerical example is provided to illustrate the effectiveness of our approach that leads to a better H∞ level compared with other results, from literature, for the same example.

scholarly journals Finite-time non-fragile controller design for a class of switching linear parameter varying systems based on linear matrix inequalities

2018 ◽  
Vol 233 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Chengcheng Ren ◽  
Longfang Li ◽  
Shuping He
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Linear Parameter Varying System

The finite-time non-fragile controller design problem is studied for a class of switching linear parameter varying system in this article. We aim to design a suitable finite-time non-fragile controller such that the closed-loop switching linear parameter varying system is finite-time bounded. Based on the linear matrix inequalities and multiple Lyapunov functions methods, sufficient conditions on the existence of the finite-time non-fragile controller are proposed and proved. Considering the parameters dependence, we change the infinite linear matrix inequalities into finite linear matrix inequalities by using approximate basis functions and gridding techniques. Finally, a simulation example is given to illustrate the effectiveness of the design methods.

scholarly journals Sliding Mode Observers Based-Simultaneous Actuator and Sensor Faults Estimation for Linear Parameter Varying Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ali Ben Brahim ◽  
Slim Dhahri ◽  
Fayçal Ben Hmida ◽  
Anis Sallami
Keyword(s):  
Sliding Mode ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
System States ◽  
Sliding Mode Observers

This paper proposes a scheme to estimate actuator and sensor faults simultaneously for a class of linear parameter varying system expressed in polytopic structure where its parameters evolve in the hypercube domain. Transformed coordinate system design is adopted to decouple faults in actuators and sensors during the course of the system’s operation coincidentally, and then two polytopic subsystems are constructed. The first subsystem includes the effect of actuator faults but is free from sensor faults and the second one is affected only by sensor faults. The main contribution is to conceive two polytopic sliding mode observers in order to estimate the system states and actuator and sensor faults at the same time. Meanwhile, in linear matrix inequality optimization formalism, sufficient conditions are derived withH∞performances to guarantee the stability of estimation error and to minimize the effect of disturbances. Therefore, all parameters of observers can be designed by solving these conditions. Finally, simulation results are given to illustrate the effectiveness of the proposed simultaneous actuator and sensor faults estimation.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

POLYTOPIC OBSERVER FOR GLOBAL SYNCHRONIZATION OF SYSTEMS WITH OUTPUT MEASURABLE NONLINEARITIES

2003 ◽  
Vol 13 (03) ◽  
pp. 703-712 ◽  
Author(s):  
GILLES MILLERIOUX ◽  
JAMAL DAAFOUZ
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
Chaos Synchronization ◽  
Observer Design ◽  
Linear Matrix ◽  
Dynamical Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Lyapunov Approach ◽  
Special Case

Chaos synchronization has been tackled by considering the problem as a special case of an observer design. The considered dynamical systems to be synchronized have measurable nonlinearities. Their dynamical matrix is described in a polytopic way. By using the notion of polyquadratic stability, the problem of the observer synthesis is turned into the resolution of a set of Linear Matrix Inequalities (LMI) which are less conservative compared to the case of an usual quadratic Lyapunov approach. This enables to enlarge the class of systems for which synchronization can take place. The resulting matrix gain of the observer is computed by interpolating vertices gains resulting from the solution of the LMI's.

Robust and Non-Fragile H∞ Observer-Based Filter Design for Parameter Uncertain System Using PLMI Approach

2013 ◽  
Vol 373-375 ◽  
pp. 685-688
Author(s):  
Seung Hyeop Yang ◽  
Seung Hyun Paik ◽  
Hong Bae Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Uncertain System ◽  
Relaxation Technique ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Polytopic Uncertainties

This paper describes the synthesis of a robust and non-fragile H∞ observer-based filter design for a class of parameter uncertain system with polytopic uncertainties, disturbances, and gain variations. We present the sufficient condition for filter existence and the method for designing a robust and non-fragile H∞ filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use the relaxation technique to find finite solutions for a robust and non-fragile H∞ filter. We show that the proposed filter can minimize the estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

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