Obtainability of closed-loop systems using constant state feedback or output feedback

1976 ◽  
Vol 12 (12) ◽  
pp. 303 ◽  
Author(s):  
V. Sinswat ◽  
F. Fallside
Keyword(s):  
Output Feedback ◽  
State Feedback ◽  
Closed Loop ◽  
Closed Loop Systems ◽  
Constant State

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

Fictitious Reference Signal Based Real-Time Update of State Feedback Gains and its Experimental Verification

2016 ◽  
Vol 28 (5) ◽  
pp. 625-632 ◽  
Author(s):  
Yuki Okano ◽  
◽  
Osamu Kaneko ◽  
Keyword(s):  
Real Time ◽  
State Feedback ◽  
Closed Loop ◽  
Reference Signal ◽  
Parameter Tuning ◽  
Closed Loop Systems ◽  
Recursive Computation ◽  
Optimal Gains ◽  
Past Data ◽  
Time Update

[abstFig src='/00280005/02.jpg' width='300' text='Real-time update of state feedback gains' ] This paper presents a new real-time parameter tuning in the data-driven framework. We focus on the tuning of state feedback gains to realize the desired performance of closed loop systems. For a real-time update tuning of this type of a controller, the notion of fictitious reference signal or the fictitious exogenous signal is utilized to generate the optimal gains in the real-time by using the measured past data. We also explain how the optimization can be realized as a recursive computation in real-time updates. Finally, an experiment is done to verify the effectiveness of the proposed method.

A New Method of Calculating the State Feedback Gain Vector of Vibration Control System

2012 ◽  
Vol 229-231 ◽  
pp. 424-427
Author(s):  
Ming Yang ◽  
De Chen Zhang ◽  
Xin Xiang Zhou
Keyword(s):  
Vibration Control ◽  
Uncertain Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Random Perturbation ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Vibration System ◽  
Deterministic Systems ◽  
Closed Loop Systems

Using the random model, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. The feedback gain matrix is determined based on the deterministic systems, and then it is applied to the actual uncertain systems. A method to calculate the standard deviations for responses of the closed-loop systems with the uncertain parameters is presented by using the random perturbation. This method is applied to a vibration system to illustrate the application. The numerical results show that the present method is effective.

scholarly journals Finite-Time H2/H∞ Control for Linear Itô Stochastic Systems with x,u,v-Dependent Noise

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Zhiguo Yan ◽  
Shiyu Zhong ◽  
Xingping Liu
Keyword(s):  
Optimization Algorithm ◽  
Finite Time ◽  
Performance Index ◽  
State Feedback ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Transient Performance ◽  
Closed Loop Systems ◽  
Linear Stochastic Systems ◽  
Finite Time Boundedness

This paper deals with the problem of the H2/H∞ control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H2/H∞ control does not involve systems’ transient performance. To express this problem clearly, a concept called finite-time H2/H∞ control is introduced. Moreover, state feedback and observer-based finite-time H2/H∞ controllers are designed, which guarantee finite-time boundedness, H2 performance index, and H∞ performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H2/H∞ control is presented to obtain the minimum values of the H2 index and H∞ index. Finally, we use an example to show the validity of the obtained results.

Mode-dependent robust and non-fragile finite-time H∞ control for nonlinear singular Markovian jump systems

2021 ◽  
pp. 014233122110350
Author(s):  
Hongping Niu ◽  
Lin Li ◽  
Pengnan Wang
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Controller ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Closed Loop Systems ◽  
Singular Markovian Jump Systems ◽  
Finite Time Boundedness ◽  
Jump Systems

This paper is concerned with the problem of mode-dependent robust and non-fragile finite-time [Formula: see text] control for a class of nonlinear singular Markovian jump systems (NSMJSs) with parameter uncertainties and time-varying norm-bounded disturbance. Some sufficient conditions ensuring the singular stochastic [Formula: see text] finite-time boundedness (SS[Formula: see text]FTB) are developed for the given system by using the stochastic analysis and linear matrix inequality techniques. Then, a finite-time [Formula: see text] state feedback controller is designed, which can guarantee the [Formula: see text] finite-time boundedness of the closed-loop systems. Furthermore, a robust and non-fragile finite-time [Formula: see text] state feedback controller is also provided to ensure the [Formula: see text] finite-time boundedness of the closed-loop systems when the controller gain has an additive perturbation. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Non-Fragile Passive Control for Nonlinear Singular Systems with Time-Delay and Uncertainties

2012 ◽  
Vol 546-547 ◽  
pp. 997-1002
Author(s):  
Hong Li ◽  
Shu Hui Shi ◽  
Ou Wu
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Closed Loop ◽  
Passive Control ◽  
Singular Systems ◽  
Feedback Controller ◽  
Numerical Example ◽  
State Feedback Controller ◽  
Nonlinear Singular Systems ◽  
Closed Loop Systems

This paper focuses on the problem of non-fragile robust passive control for a class of nonlinear singular systems which contain structure uncertainties and time delay. A memorial state feedback controller is considered, and the controller is constructed such that closed-loop systems are generalized quadratically stable and passive with dissipation. The algorithm is given for obtaining the maximum dissipation, at the same time, the maximum guaranteed dissipation controller is proposed. Numerical example is presented to show the validity and applicability of the proposed method.

Stabilization Conditions for a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Sunhua Huang ◽  
Bin Wang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Lyapunov Stability Theorem ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Closed Loop Systems

The stabilization problem of fractional-order nonlinear systems for 0<α<1 is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.

Output Feedback Adaptive Maneuvering for Nonlinear MIMO Systems with High Frequency Gain Matrix Hurwitz

2011 ◽  
Vol 383-390 ◽  
pp. 2417-2422
Author(s):  
Ying Zhou ◽  
Qiang Zang
Keyword(s):  
Output Feedback ◽  
High Frequency ◽  
Closed Loop ◽  
Mimo Systems ◽  
Positive Definite ◽  
Vector Form ◽  
Gain Matrix ◽  
Closed Loop Systems ◽  
Backstepping Approach ◽  
Control Scheme

In this paper, the adaptive maneuvering control based on output feedback is studied for uncertain nonlinear multi-input multi-output (MIMO) systems. The high frequency gain matrix of the systems only needs to be Hurwitz, which relaxes the positive definite limitation in the existing results. Based on the backstepping approach with vector form, an output feedback adaptive maneuvering control scheme is proposed. The geometric and the dynamic tasks are solved meanwhile the global stability of the closed-loop systems is guaranteed through the proposed control scheme.

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