Design of state feedback controller for discrete linear systems with time delay

2013 ◽  
Author(s):  
Shuaitian He ◽  
Bingkun Jiang
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
State Feedback ◽  
Feedback Controller ◽  
State Feedback Controller ◽  
Discrete Linear Systems

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

2018 ◽  
Vol 28 (03) ◽  
pp. 1850042 ◽  
Author(s):  
Xin-You Meng ◽  
Yu-Qian Wu
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
State Feedback ◽  
Critical Value ◽  
Feedback Controller ◽  
Bifurcation Parameter ◽  
State Feedback Controller ◽  
Interior Equilibrium ◽  
Fish Model ◽  
Singularity Induced Bifurcation

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

scholarly journals Finite-Time Control of Networked Control Systems with Time Delay and Packet Dropout

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yerong Sun ◽  
Yeguo Sun ◽  
Chunzhi Yang
Keyword(s):  
Control System ◽  
Time Delay ◽  
Control Theory ◽  
Control Systems ◽  
Finite Time ◽  
State Feedback ◽  
Network Control ◽  
Feedback Controller ◽  
Network Control System ◽  
State Feedback Controller

This paper studies the finite-time stabilization and boundedness problem of a class of network control systems that are simultaneously affected by time delay and packet loss. Based on the Lyapunov function method, the sufficient conditions for the design of the state feedback controller in the form of linear matrix inequality are obtained. The state feedback controller makes the network control system stable for a finite time. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the method. The research results of this paper will develop and enrich the control theory system of the network control system and provide advanced control theory methods and application technology reserves in order to promote the development process of the network control system application and improve the application level.

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