scholarly journals Admissibility Analysis and Controller Design for Discrete Singular Time-Delay Systems Embracing Uncertainties in the Difference and Systems’ Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Chih-Peng Huang
Keyword(s):  
Controller Design ◽  
Singular System ◽  
Delay System ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Admissibility Condition ◽  
The Difference ◽  
Singular Time

This paper mainly investigates the admissibility analysis and the admissibilizing controller design for the uncertain discrete singular system with delayed state. Based on Lyapunov–Krasovskii stability theory, an original admissibility condition for the nominal singular delay system is first presented. By involving the uncertainties in both difference and system matrices simultaneously, we devote to analyzing the robust admissibility for the regarded uncertain discrete singular system with delayed state. Furthermore, by hiring the state feedback control law, we further discuss the admissibilizing controller design for the resulting closed-loop system. Since all the derived criteria are expressed in terms of strict linear matrix inequalities (LMIs) or parametric LMIs, we thus can handily verify them via current LMI solvers. Finally, two numerical examples are given to illustrate the effectiveness and validity of the proposed approach.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation

2018 ◽  
Vol 25 (4) ◽  
pp. 868-881 ◽  
Author(s):  
Maryam Sadat Asadinia ◽  
Tahereh Binazadeh ◽  
Behrouz Safarinejadian
Keyword(s):  
Time Delay ◽  
Singular Systems ◽  
Singular System ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Analysis And Design ◽  
Singular Time

This paper investigates the problem of delay-range-dependent robust stabilization for nonlinear singular systems with time-delay subject to some constraints. In practice, the control problem of dynamic systems faces a variety of constraints such as: presence of input saturation; one-sided Lipschitz nonlinearities; model uncertainties; and time-varying delay. The interaction of both algebraic and differential equations in singular systems with delayed state variables adds some complexities and difficulties in the procedure of analysis and design of singular time-delay systems. Moreover, the one-sided Lipschitz nonlinearity condition, which is less conservative than the well-known Lipschitz condition, is considered while the presence of actuator saturation also imposes additional complexity in the procedure of controller design. In this regard, by choosing an appropriate Lyapunov–Krasovskii functional with applying the free-weighting matrices approach, the sufficient conditions are derived as linear matrix inequalities which guarantee the asymptotic stability of the resulting uncertain closed-loop singular system. Finally, computer simulations are provided to verify the theoretical results.

Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

2015 ◽  
Vol 3 (5) ◽  
pp. 472-480
Author(s):  
Huainian Zhu ◽  
Guangyu Zhang ◽  
Chengke Zhang ◽  
Ying Zhu ◽  
Haiying Zhou
Keyword(s):  
Time Delay ◽  
Decision Makers ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Linear Quadratic ◽  
Nash Game ◽  
Multiple Decision Makers ◽  
Nash Strategies ◽  
Singular Time

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

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 Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linna Zhou ◽  
Qianjin Wang ◽  
Xiaoping Ma ◽  
Chunyu Yang
Keyword(s):  
Switched Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Singularly Perturbed ◽  
Dynamic State ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Stability Bound ◽  
Takagi Sugeno

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

2011 ◽  
Author(s):  
Xin Wang ◽  
Edwin E. Yaz ◽  
Susan C. Schneider ◽  
Yvonne I. Yaz
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Time Step ◽  
Control Approach ◽  
The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

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 Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. Rajchakit ◽  
P. Niamsup ◽  
T. Rojsiraphisal ◽  
G. Rajchakit
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Performance Measure ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Guaranteed Cost

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Dissipative Control for Nonlinear Neutral Delay Systems

2011 ◽  
Vol 48-49 ◽  
pp. 439-442
Author(s):  
Long Liu ◽  
Ming Li
Keyword(s):  
Controller Design ◽  
Design Method ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Neutral Delay ◽  
Static State ◽  
Neutral Delay Systems ◽  
Dissipative Control ◽  
Static State Feedback

The problem of delay-dependent dissipative control for nonlinear neutral delay systems is dealt with. We develop the design method of dissipative static state feedback controller such that the closed-loop system is absolutely stable and strictly-dissipative. Sufficient conditions for the existence of the quadratic dissipative controller are obtained by using linear Matrix Inequality(LMI) approach. Furthermore, a procedure of constructing such a controller from the solution of LMI is given. It is shown that the solvability of a dissipative controller design is implied by the feasibility of LMIs.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

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