scholarly journals General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yiheng Wei ◽  
Hamid Reza Karimi ◽  
Shu Liang ◽  
Qing Gao ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Linear Time ◽  
Output Feedback Control ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Linear Time Invariant ◽  
Output Feedback Stabilization ◽  
Closed Loop Systems

This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI) systems with the fractional commensurate order0<α<2. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI) are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with0<α<1. Furthermore, the results are extended to stabilize the FO-LTI systems with1≤α<2. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

Output Feedback Stabilization Based on General Solution of Matrix Equation

2012 ◽  
Vol 546-547 ◽  
pp. 903-909
Author(s):  
Hai Bin Shi ◽  
Li Qi
Keyword(s):  
General Solution ◽  
Output Feedback ◽  
Matrix Equation ◽  
Linear Time ◽  
Free Variable ◽  
Feedback Stabilization ◽  
Gain Matrix ◽  
Linear Time Invariant ◽  
Output Feedback Stabilization ◽  
Linear Time Invariant Systems

This paper gives a method for static output feedback stabilization of linear time invariant systems. A general solution of a matrix equation concerning system parameter matrices is used to construct a state coordinate transformation. Then, the closed-loop system is equivalent to a transitional form, whose pivotal isolated subsystem can be stabilized via a gain matrix. This gain matrix is the free variable of the general solution. Furthermore, using this general solution of the matrix equation, the original problem is reformulated to a low dimension system, which can be easily solved. Numerical example is given to illustrate the validity of the proposed algorithm.

scholarly journals Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

2020 ◽  
Vol 42 (16) ◽  
pp. 3168-3182
Author(s):  
Okan Demir ◽  
Hitay Özbay
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Mixed Integer ◽  
Static Output Feedback ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Linear ◽  
Static Output

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

Nonfragile H∞ Output Feedback Controller Design for Linear Systems*

2003 ◽  
Vol 125 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Guang-Hong Yang ◽  
Jian Liang Wang
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Linear Time ◽  
Output Feedback Control ◽  
Disturbance Attenuation ◽  
Output Measurement ◽  
Linear Time Invariant ◽  
Measurement Feedback ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This paper is concerned with the nonfragile H∞ controller design problem for linear time-invariant systems. The controller to be designed is assumed to have norm-bounded uncertainties. Design methods are presented for dynamic output (measurement) feedback. The designed controllers with uncertainty (i.e. nonfragile controllers) are such that the closed-loop system is quadratically stable and has an H∞ disturbance attenuation bound. Furthermore, these robust controllers degenerate to the standard H∞ output feedback control designs, when the controller uncertainties are set to zero.

A Passive Fault-Tolerant Switched Control Approach for Linear Multivariable Systems: Application to a Quadcopter Unmanned Aerial Vehicle Model

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Hasan Başak ◽  
Emre Kemer ◽  
Emmanuel Prempain
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
Fault Tolerant ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Passive State ◽  
Linear Matrix ◽  
Control Approach ◽  
Linear Time Invariant ◽  
L2 Norm

Abstract This paper proposes synthesis algorithms for the design of passive state- and output-feedback fault-tolerant controllers. Sufficient conditions for the existence and the construction of such fault-tolerant controllers are given in terms of linear matrix inequalities (LMIs) which can be solved efficiently. The state-feedback fault-tolerant controller consists of a family of state-feedback gains switched appropriately according to a stabilizing switching signal so that the closed-loop system satisfies a performance requirement expressed in terms of system L2 norm. Similarly, the output feedback controller consists of a family of full-order linear, time-invariant controllers switched according to a stabilizing signal that depends only on the controller states. Both approaches are passive in the sense that they do not rely on the detection and/or the estimation of the faults. The proposed approaches are tested on a nonlinear model of a quadcopter. Simulation results show that satisfactory stability, tracking, and disturbance rejection are maintained despite of time-varying actuator faults.

scholarly journals Weighted Consensus Problem for Multiagent Systems with Edge- and Node-Weighted Directed Graphs

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Lixin Gao ◽  
Hui Fang ◽  
Wenhai Chen ◽  
He Cao
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
Linear Time ◽  
Control Strategies ◽  
Directed Graphs ◽  
Output Feedback Control ◽  
Linear Time Invariant ◽  
Special Cases ◽  
Cluster Consensus ◽  
Bipartite Consensus

In this paper, the concept of consensus is generalized to weighted consensus, by which the conventional consensus, the bipartite consensus, and the cluster consensus problems can be unified in the proposed weighted consensus frame. The dynamics of agents are modeled by the general linear time-invariant systems. The interaction topology is modeled by edge- and node-weighted directed graphs. Under both state feedback and output feedback control strategies, the weighted consensus problems are transformed into the equivalent conventional consensus problems. Then, some distributed state feedback and output feedback protocols are proposed to solve the weighted consensus problems. For output feedback case, a unified frame to construct the state-observer-based weighted consensus protocols is proposed, and different design approaches are discussed. As special cases, some related results for bipartite consensus and cluster consensus can be obtained directly. Finally, a simple example is given to illustrate the effectiveness of our proposed approaches.

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