scholarly journals Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

2020 ◽  
Vol 36 (1) ◽  
pp. 69-88
Author(s):  
Ho Pham Huy Anh ◽  
Cao Van Kien
Keyword(s):  
Lyapunov Function ◽  
Fuzzy System ◽  
Controller Design ◽  
Descriptor Systems ◽  
Descriptor System ◽  
System A ◽  
Novel Approach ◽  
Special Cases ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical Systems

This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.

scholarly journals Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

2020 ◽  
Vol 36 (1) ◽  
pp. 69-88
Author(s):  
Ho Pham Huy Anh ◽  
Cao Van Kien
Keyword(s):  
Lyapunov Function ◽  
Fuzzy System ◽  
Controller Design ◽  
Descriptor Systems ◽  
Descriptor System ◽  
System A ◽  
Novel Approach ◽  
Special Cases ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical Systems

This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.

Synchronization of Multiple Chaotic Gyroscopes Using the Fundamental Equation of Mechanics

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Byungrin Han
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Mechanical Systems ◽  
Fundamental Equation ◽  
Nonlinear Dynamical ◽  
Novel Approach ◽  
Highly Nonlinear ◽  
Nonlinear Mechanical ◽  
Fundamental Equation Of Mechanics ◽  
Control Forces ◽  
Nonlinear Mechanical Systems

This paper provides a simple, novel approach for synchronizing the motions of multiple “slave” nonlinear mechanical systems by actively controlling them so that they follow the motion of an independent “master” mechanical system. The multiple slave systems need not be identical to one another. The method is inspired by recent results in analytical dynamics, and it leads to the determination of the set of control forces to create such synchronization between highly nonlinear dynamical systems. No linearizations or approximations are involved, and the exact control forces needed to synchronize the nonlinear systems are obtained in closed form. The method is applied to the synchronization of multiple, yet different, chaotic gyroscopes that are required to replicate the motion of a master gyro, which may have a chaotic or a regular motion. The efficacy of the method and its simplicity in synchronizing these mechanical systems are illustrated by two numerical examples, the first dealing with a system of three different gyros, the second with five different ones.

Stability Analysis and Controller Design for Fuzzy Parameter Varying Systems Based on Fuzzy Lyapunov Function

2018 ◽  
Author(s):  
Xiaojun Ban ◽  
Hongyang Zhang ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Controller Design ◽  
Design Procedure ◽  
Handling Time ◽  
Feedback Gain ◽  
Time Varying ◽  
System A ◽  
Fuzzy Lyapunov Function ◽  
Parameter Varying ◽  
Fuzzy Parameter

The fuzzy parameter varying (FPV) system is a mathematical model proposed to handle nonlinear time-varying dynamical systems encountered in engineering, which has some essential advantages in handling time-varying models. In this article, a new relaxation approach is proposed for the analysis and controller design of the FPV system. Different from the current results on the FPV system, the proposed approach employs the fuzzy Lyapunov function and full block S-procedure to reduce the conservatism in analysis. Furthermore, the relaxation technique proposed in this article can be also used in solving controller synthesis problem effectively. As a result, a design procedure of non-PDC output feedback gain-scheduling controller is provided to ensure asymptotic stability of the closed-loop FPV system. A numerical example is provided to illustrate the proposed method.

scholarly journals Impulse Elimination and Fault-Tolerant Preview Controller Design for a Class of Descriptor Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chen Jia ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Controller Design ◽  
Fault Tolerant ◽  
Original System ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Equivalent Transformation ◽  
Sensor Faults ◽  
Augmented System ◽  
Model Following ◽  
General Method

In this paper, a fault-tolerant preview controller is designed for a class of impulse controllable continuous time descriptor systems with sensor faults. Firstly, the impulse is eliminated by introducing state prefeedback; then an algebraic equation and a normal control system are obtained by restricted equivalent transformation for the descriptor system after impulse elimination. Next, the model following problem in fault-tolerant control is transformed into the optimal regulation problem of the augmented system which is constructed by a general method. And the final augmented system and its corresponding performance index function are obtained by state feedback for the augmented system constructed above. The controller with preview effect for the final augmented system is attained based on the existing conclusions of optimal preview control; then, the fault-tolerant preview controller for the original system is obtained through integral and backstepping. The relationships between the stabilisability and detectability of the final augmented system and the corresponding characteristics of the original descriptor system are also strictly discussed. The effectiveness of the proposed method is verified by numerical simulation.

scholarly journals SpecificD-Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Chih-Peng Huang
Keyword(s):  
Controller Design ◽  
State Space Model ◽  
Parametric Uncertainty ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Closed Loop Systems ◽  
Derivative Matrix ◽  
Feasible Solutions ◽  
Necessary And Sufficient

Stability analysis issues and controller synthesis for descriptor systems with parametric uncertainty in the derivative matrix are discussed in this paper. The proposed descriptor system can extend the system’s modeling extent of physical and engineering systems from the traditional state-space model. First, based on the extendedD-stability definitions for the descriptor model, necessary and sufficient admissibility andD-admissibility conditions for the unforced nominal descriptor system are derived and formulated by compact forms with strict linear matrix inequality (LMI) manner. In contrast, existing results need to involve nonstrict LMIs, which cannot be evaluated by current LMI solvers and need some extra treatments. Deducing from the obtained distinct results, the roust admissibility andD-admissibility of the descriptor system with uncertainties in both the derivative matrix and the system’s matrices thus can be coped. Furthermore, by involving a proportional and derivative state feedback (PDSF) control law, we further address the controller design for the resulting closed-loop systems. Since all the proposed criteria are explicitly expressed in terms of the strict LMIs, we can use applicable LMI solvers for evaluating the feasible solutions. Finally, the efficiency and practicability of the proposed approach are demonstrated by two illustrative examples.

scholarly journals General Solutions for Descriptor Systems of Coupled Generalized Sylvester Matrix Fractional Differential Equations via Canonical Forms

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 283 ◽  
Author(s):  
Kanjanaporn Tansri ◽  
Pattrawut Chansangiam
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Fractional Differential Equations ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Sylvester Matrix ◽  
Special Cases ◽  
Matrix Differential Equations ◽  
Fractional Differential ◽  
Single Matrix

We investigate a descriptor system of coupled generalized Sylvester matrix fractional differential equations in both non-homogeneous and homogeneous cases. All fractional derivatives considered here are taken in Caputo’s sense. We explain a 4-step procedure to solve the descriptor system, consisting of vectorization, a matrix canonical form concerning ranks, and matrix partitioning. The procedure aims to reduce the descriptor system to a descriptor system of fractional differential equations. We also impose a condition on coefficient matrices, related to the symmetry of the solution for descriptor systems. It follows that an explicit form of its general solution is given in terms of matrix power series concerning Mittag–Leffler functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases. In particular, we obtain an alternative procedure to solve linear continuous-time descriptor systems via a matrix canonical form.

scholarly journals Delay-Dependent Finite-TimeH∞Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Baoyan Zhu ◽  
Jingjun Zhang ◽  
Daqing Zhang ◽  
Aibin Liu
Keyword(s):  
Closed System ◽  
Finite Time ◽  
Controller Design ◽  
Fuzzy Model ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Time Interval ◽  
Impulsive Behavior ◽  
Finite Time Interval ◽  
Delay Dependent

Delay-dependent finite-timeH∞controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-timeH∞controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds theH∞performance to a prescribed disturbance attenuation levelγ. The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve aH∞performance level.

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