scholarly journals The Mathematical Study of Pest Management Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jinbo Fu ◽  
Yanzhen Wang
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Pest Management ◽  
Management Strategy ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Successor Function ◽  
Mathematical Study ◽  
The Mathematical Model

The theory of impulsive state feedback control is used to establish a mathematical model in the pest management strategy. Then, the qualitative analysis of the mathematical model was provided. Here, a successor function in the geometry theory of differential equations is used to prove the sufficient conditions for uniqueness of the 1-periodic solution. It proved the orbital asymptotic stability of the periodic solution. In addition, numerical analysis is used to discuss the application significance of the mathematical model in the pest management strategy.

scholarly journals A Pest Management Model with Stage Structure and Impulsive State Feedback Control

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Guoping Pang ◽  
Zhiqing Liang ◽  
Weijian Xu ◽  
Lijie Li ◽  
Gang Fu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Pest Management ◽  
State Feedback ◽  
Stage Structure ◽  
State Feedback Control ◽  
Management Model ◽  
Continuous Systems ◽  
Impulsive State Feedback Control ◽  
The Stability

A pest management model with stage structure and impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semicontinuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

scholarly journals Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Zhong Zhao ◽  
Liuyong Pang ◽  
Zhanping Zhao ◽  
Chengguang Luo
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Microbial Degradation ◽  
State Feedback ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Control Measures ◽  
Positive Order ◽  
Impulsive State Feedback Control

The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.

scholarly journals Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chunjin Wei ◽  
Lansun Chen
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Functional Response ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Impulsive State Feedback Control ◽  
Predator Model ◽  
Order One Periodic Solution

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.

Sampled-Data State Feedback Stabilization of Boolean Control Networks

2016 ◽  
Vol 28 (4) ◽  
pp. 778-799 ◽  
Author(s):  
Yang Liu ◽  
Jinde Cao ◽  
Liangjie Sun ◽  
Jianquan Lu
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Global Stabilization ◽  
Sampled Data ◽  
Control Networks ◽  
Piecewise Constant Control ◽  
Necessary And Sufficient

In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.

Impulsive state feedback control during the sulphitation reaction in process of manufacture of sugar

2020 ◽  
pp. 2050076
Author(s):  
Guoping Pang ◽  
Xianbo Sun ◽  
Zhiqing Liang ◽  
Silian He ◽  
Xiaping Zeng
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Limit Cycles ◽  
Switched Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Continuous Systems ◽  
Stability Criteria ◽  
Impulsive State Feedback Control ◽  
Existence And Stability

In this paper, the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacture of sugar is considered. By means of square approximation and a series of switched systems, the periodic solution is approximated by a series of continuous hybrid limit cycles. Similar to the analysis of limit cycles of continuous systems, the existence and stability criteria of the order-1 periodic solution are obtained. Further, numerical analysis and discussion are given.

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.

scholarly journals Stability of stochastic systems with jumps

1996 ◽  
Vol 3 (2) ◽  
pp. 173-185 ◽  
Author(s):  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Brownian Motion ◽  
Control Strategy ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
And Brownian Motion ◽  
Quadratic Stabilization ◽  
Guaranteed Cost ◽  
Linear And Nonlinear Systems

This paper deals with stochastic stability of systems with Markovian jumps and Brownian motion. Mainly, we present sufficient conditions for quadratic stabilization of Ito type stochastic linear and nonlinear systems with Markovian jumps and Brownian motion using state feedback control. We also prove the guaranteed cost property of the proposed control strategy for the linear case.

Disturbance Rejection With Simultaneous Input-Output Linearization and Decoupling Via Restricted State Feedback

1997 ◽  
Vol 122 (1) ◽  
pp. 49-62 ◽  
Author(s):  
A. S. Tsirikos ◽  
K. G. Arvanitis
Keyword(s):  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
State Feedback Control ◽  
Systems Of Equations ◽  
Input Output ◽  
Control Laws ◽  
Simultaneous Input ◽  
Input Output Linearization

The disturbance rejection with simultaneous input-output linearization and decoupling problem of nonsquare nonlinear systems via restricted state feedback is investigated in this paper. The problem is treated on the basis of an algebraic approach whose main feature is that it reduces the determination of the admissible state feedback control laws to the solution of an algebraic and a first order partial differential systems of equations. Verifiable necessary and sufficient conditions of algebraic nature based on these systems of equations are established for the solvability of the aforementioned problem. Moreover, an explicit expression for a special admissible restricted state feedback controller is analytically derived. [S0022-0434(00)02101-8]

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