Stabilizing Controllers for Uncertain Linear Saturating Systems With Additive Disturbances

1991 ◽  
Vol 113 (2) ◽  
pp. 334-336 ◽  
Author(s):  
Jyh-Horng Chou ◽  
Ing-Rong Horng
Keyword(s):  
State Feedback ◽  
Uncertain System ◽  
Lyapunov Equation ◽  
Upper Bounds ◽  
State Feedback Control ◽  
System Response ◽  
Control Law ◽  
Time Varying ◽  
Stabilizing Controllers ◽  
Linear State

In this technical brief, the stabilization of an uncertain system with a saturating actuator and an additive disturbance is discussed. The uncertainties and the additive disturbances may be linear, nonlinear, and/or time-varying, but only the upper bounds are assumed known. A linear state feedback control law stabilizes the uncertain system with additive disturbance, and guarantees that, ultimately, the system response lies in a neighborhood of the origin. But the neighborhood cannot be arbitrarily made small by the linear state feedback controller. The proposed approach does not need the solution of a Lyapunov equation or a Riccati equation, therefore the computational burden can be decreased. An example illustrates the application of the proposed method.

Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound

2010 ◽  
Vol 40-41 ◽  
pp. 103-110
Author(s):  
Jie Jin
Keyword(s):  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Linear State ◽  
Varying Delay ◽  
Nonlinear Delay

This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

Optimal Linear State Feedback Time-Varying Regulator for a Unicycle Mobile Robot

2008 ◽  
Author(s):  
Elvira Rafikova ◽  
Paulo R. G. Kurka ◽  
Marat Rafikov
Keyword(s):  
Mobile Robot ◽  
State Feedback ◽  
Control Design ◽  
State Feedback Control ◽  
Optimal Time ◽  
Control Law ◽  
Time Varying ◽  
Optimal Linear ◽  
Linear State ◽  
Feedback Time

This paper proposes an optimal time-varying linear state feedback control for wheeled mobile robot of the unicycle type. The control law that stabilizes exponentially the motion of the robot to a given desired trajectory is found, after transformation of the cinematic model of the robot into a well-known Brocket integrator [1]. Numerical simulations are presented in order to demonstrate the effectiveness of the proposed control design.

scholarly journals Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system

2005 ◽  
Vol 46 (4) ◽  
pp. 471-484 ◽  
Author(s):  
Honglei Xu ◽  
Xinzhi Liu ◽  
Kok Lay Teo
Keyword(s):  
Feedback Control ◽  
Switched Systems ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
State Model ◽  
Control Law ◽  
Time Varying ◽  
Impulsive Switched Systems ◽  
Bounded Uncertainty

AbstractIn this paper, we study the problem of robust H∞ stabilisation with definite attenuance for a class of impulsive switched systems with time-varying uncertainty. A norm-bounded uncertainty is assumed to appear in all the matrices of the state model. An LMI-based method for robust· H∞ stabilisation with definite attenuance via a state feedback control law is developed. A simulation example is presented to demonstrate the effectiveness of the proposed method.

scholarly journals An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
P. Bumroongsri
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Control Laws ◽  
Lpv Systems ◽  
Parameter Dependent ◽  
Dependent State

An offline model predictive control (MPC) algorithm for linear parameter varying (LPV) systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI) optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

2015 ◽  
Vol 82 (1-2) ◽  
pp. 349-355 ◽  
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf ◽  
Mohamed Ali Hammami ◽  
Abderrazak Ouali
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

scholarly journals The Practical Stabilization for a Class of Networked Systems with Actuator Saturation and Input Additive Disturbances

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Dongyan Chen ◽  
Shanqiang Li ◽  
Yujing Shi
Keyword(s):  
Feedback Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Control Law ◽  
Equation Approach ◽  
Linear State ◽  
Practical Stabilization

The practical stabilization problem is investigated for a class of linear systems with actuator saturation and input additive disturbances. Firstly, the case of the input additive disturbance being a bounded constant and a variety of different situations of system matrices are studied for the three-dimensional linear system with actuator saturation, respectively. By applying the Riccati equation approach and designing the linear state feedback control law, sufficient conditions are established to guarantee the semiglobal practical stabilization or oscillation for the addressed system. Secondly, for the case of the input additive disturbances being time-varying functions, a more general class of systems with actuator saturation is investigated. By employing the Riccati equation approach, a low-and-high-gain linear state feedback control law is designed to guarantee the global or semiglobal practical stabilization for the closed-loop systems.

scholarly journals Stabilization of Switched Linear Systems with Control Constraints Based on EA

2020 ◽  
Author(s):  
Hosni Houssem ◽  
Ben Mabrouk Walid ◽  
Liouane Noureddine
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Previous Method ◽  
State Feedback Control ◽  
Control Law ◽  
Control Constraints ◽  
Switched Linear Systems ◽  
Stabilizing Controllers ◽  
Output Feedback Controller ◽  
The Stability

In this paper, we address the problem of stabilization of switched linear systems. The idea is to look for a state feedback control law using evolutionary algorithms (EA) in order to assure the stability of the switched linear systems under control constraints. In some cases when states are not available and only outputs are measurable, the previous method is applied to design an output feedback controller which stabilizes the system. Both stabilizing controllers are developed using deferential evolution and genetic algorithm. Two numerical examples illustrate our proposed theory and point out the effectiveness of our proposed approaches.

Guaranteed Asymptotic Output Stability for Systems With Constant Disturbances

1987 ◽  
Vol 109 (2) ◽  
pp. 186-189 ◽  
Author(s):  
W. E. Schmitendorf ◽  
B. R. Barmish
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
State Feedback ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Control Law ◽  
Uncertain Parameters ◽  
Output Stability ◽  
Linear State ◽  
Parameter Values

For a class of linear systems in which there are uncertain parameters in the system and input matrices, as well as constant additive disturbances, a linear state feedback control law is derived. The only information available about the uncertain parameters is the bounding sets in which they lie. The design guarantees that the specified output approaches zero for all possible parameter values and for all initial conditions. Two examples illustrate the application of the theory.

Robust H2/H∞Control Strategy for Linear Markovian Jump Systems

2014 ◽  
Vol 525 ◽  
pp. 646-652
Author(s):  
Min Bian ◽  
Qing Yun Guo
Keyword(s):  
Control Strategy ◽  
State Feedback ◽  
Control Strategies ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Bounded Real Lemma ◽  
Finite State ◽  
Linear State ◽  
Feasible Solutions ◽  
Jump Systems

The robust H2/<em>H</em>∞ control strategy for a class of linear continuous-time uncertain systems with randomly jumping parameters is investigated. The transition of the jumping parameters is decided by a finite-state Markov process. The uncertainties are supposed to be norm-bounded. It is desired to design a linear state feedback control strategies such that the closed-loop system satisfies H performance and minimizes the H2 norm of the system. A sufficient condition is first established on the existence of the robust H2/<em>H</em>∞controller bases on the bounded real lemma. Then the corresponding state-feedback law is given in terms of a set of linear matrix inequalities (LMIs). It is showed that this condition is equivalent to the feasible solutions problem of LMI. Furthermore, the control strategy design problem is converted into a convex optimization problem subject to LMI constraints, which can be easily solved by standard numerical software.

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