scholarly journals Advanced controller design for uncertain linear systems with time-varying delays via augmented zero equality approach

2021 ◽  
Author(s):  
YongGwon Lee ◽  
Youngjae Kim ◽  
Seungho Kim ◽  
Seunghoon Lee ◽  
Myeongjin Park ◽  
...  
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Controller Gain ◽  
The Stability ◽  
Uncertain Linear Systems

This paper deals with the stability analysis and controller design for linear systems with time-varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov-Krasovskii functionals, a set of Linear Matrix inequalities is derived to get advanced feasible region of stability, and controller gain matrices which guarantee the asymptotic stability of the concerned systems within maximum bound of time-delays and its time-derivative. To further reduce the conservatism of stabilization criterion a recently developed mathematical technique which constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

scholarly journals New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Yang ◽  
Chen-xin Fan
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Integral Term ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.

H∞ State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Ji Huang ◽  
Yang Shi
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump Linear Systems

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the H∞ control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.

Tracking control for the helicopter with time-varying disturbance and input stochastic perturbation

2019 ◽  
Vol 234 (4) ◽  
pp. 961-976
Author(s):  
Yankai Li ◽  
Mou Chen ◽  
Tao Li ◽  
Huijiao Wang
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Controller Design ◽  
Stochastic Perturbation ◽  
Linear Matrix ◽  
Time Varying ◽  
Inequality Technique ◽  
Error System ◽  
Feedforward Controller ◽  
The Stability

In this paper, the tracking control problem is investigated for the helicopter under time-varying disturbance, input stochastic perturbation, and unmeasurable flapping motion states. Firstly, a state observer and a disturbance observer are constructed to estimate the unmeasurable states and the time-varying disturbance, and the estimation of the disturbance is used in the feedforward controller design. Secondly, under the input stochastic perturbation, a feedback controller is constructed to guarantee the stochastic stability of the closed-loop error system. Using the stochastic control theory and the linear matrix inequality technique, the stability of the closed-loop error system is analyzed, and the gain of the controller is acquired via a solvable sufficient condition. Finally, an example is presented to illustrate the effectiveness of the proposed method.

scholarly journals Robust H∞ Consensus Control for Linear Discrete-Time Swarm Systems with Parameter Uncertainties and Time-Varying Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiao Jia ◽  
Laihong Hu ◽  
Fujun Feng ◽  
Jun Xu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Convergence Result ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Consensus Analysis ◽  
The Stability

Robust H∞ consensus control problems of linear swarm systems with parameter uncertainties and time-varying delays are investigated. In this literature, a linear consensus protocol for high-order discrete-time swarm systems is proposed. Firstly, the robust H∞ consensus control problem of discrete-time swarm systems is transformed into a robust H∞ control problem of a set of independent uncertain systems. Secondly, sufficient linear matrix inequality conditions for robust H∞ consensus analysis of discrete-time swarm systems are given by the stability theory, and a H∞ performance level γ is determined meanwhile. Thirdly, the convergence result is derived as a final consensus value of swarm systems. Finally, numerical examples are presented to demonstrate theoretical results.

scholarly journals Stability Analysis of Linear Systems under Time-Varying Samplings by a Non-Standard Discretization Method

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 278 ◽  
Author(s):  
Xiefu Jiang ◽  
Zongming Yin ◽  
Jinjing Wu
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Time Varying ◽  
Discretization Method ◽  
Sampled Data ◽  
Discrete Time System ◽  
Parameter Uncertainties ◽  
The Stability

This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.

scholarly journals Analysis on Passivity for Uncertain Neural Networks with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
O. M. Kwon ◽  
M. J. Park ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Uncertain Neural Networks

The problem of passivity analysis for neural networks with time-varying delays and parameter uncertainties is considered. By the consideration of newly constructed Lyapunov-Krasovskii functionals, improved sufficient conditions to guarantee the passivity of the concerned networks are proposed with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via two numerical examples by the comparison of maximum allowable delay bounds.

scholarly journals New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Piyapong Niamsup ◽  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Continuous Functions ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Switched Linear Systems

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

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