Robust Stabilization Method Research Articles

Advanced Control Strategy for the Visual Servoing Scheme

A general framework to compute a kinematic visual servoing controller for a general hand-eye system is proposed. The approach is based on the combination of both robust quadratic stabilization methods and saturation nonlinearities representations via the use of differential inclusion results. The design of a stabilizing controller and the determination of an associated region of stability is carried out in spite of uncertainty on the interaction screw, bounds on actuator velocities and limits on visual signal errors. The result is deduced from the resolution of matrix inequalities.

A linear matrix inequality approach for robust control of systems with delayed states

Abstract This paper addresses the robust stabilization problem for uncertain systems with delayed states. The parameter uncertainties are unknown but norm-bounded and the delay is time-varying. In this study, a linear matrix inequality (LMI) approach for robust stability analysis for the nominal unforced system and a method for robust stabilization for a class of uncertain delay systems via linear memoryless state feedback control are presented. The results depend on the size of the delay and are given in terms of linear matrix inequalities.

Discrete-time method for robust global stabilization of induction motor

The paper considers the problem of regulation of velocity and rotor flux norm of an induction motor. The rotor flux is assumed unmeasurable, load torque and rotor resistance may be unknown and time varying, with small non-differentiable disturbances present. A simple and robust discrete-time control technique is justified theoretically and tested experimentally. It can be considered as a generalization and modification of field oriented control. In its ‘non-adaptive’ modification, it ensures global exponential stability of a closed-loop system, if at least local stabilization of the system by static control is possible, for given parameter estimates. In adaptive version it provides identification and global exponential stabilization of the system. Copyright © 2000 John Wiley & Sons, Ltd.

Robust stabilization of nonlinear uncertain systems with multiple delays

In this paper, a method for robust stabilization is firstly presented for the uncertain linear systems with multiple-state delay. An extension to nonlinear delay systems subject to unmatched and matched uncertainties is extensively investigated. The state feedback controller is constructed via the solution of Riccati matrix equation and known bounding functions of the uncertainties. The proposed schemes are simple since only algebraic Riccati equations need to be solved. Finally, a numerical example is given to illustrate the results.

Delay-dependent robust [formula omitted] control of uncertain linear state-delayed systems

This paper examines the problems of robust stabilization and robust H∞ control for linear systems with a constant time delay in the state and subject to parameter uncertainty. Systems with norm-bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers. We develop methods of robust stabilization and robust H∞ control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities. The proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays.

Robust stability and stabilization of linear delayed systems with structured uncertainty

This paper shows criteria for robust stability and stabilization of linear state-delayed systems with structured uncertainty. We consider the structured uncertainty composed of repeated scalar-block and full-block forms and a time-varying state delay. Delay-dependent methods for robust stability and stabilization are provided in terms of linear matrix inequalities. For linear systems with structured uncertainty and a time-varying state delay, the proposed methods give less conservative results than those obtained via the methods accounting for only norm-boundedness of the uncertainty.

Constrained quadratic stabilization of discrete-time uncertain non-linear multi-model systems using piecewise affine state-feedback

In this paper a method for non-linear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the statespace known as clusters the plant is assumed to be an element in a polytope whose vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to being linear systems. The clusters cover the region of interest in the state-space. A n affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a single non-convex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed loop. The feasibility problem is attacked by a branch-and-bound-based global approach. If the feasibility check is successful, the Lyapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained non-linear model predictive control is presented. In addition, the control design method is applied to a simple example.

Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.

Robust output feedback stabilizability via controller switching

The paper considers the output feedback robust stabilizability problem for uncertain dynamical systems. The uncertain system under consideration is a composite of a continuous-time plant and a switched controller. A necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a Riccati algebraic equation of the H^~ filtering type. A real time implementable method for robust stabilization is also presented.

Delay-Dependent Robust Stabilization of Uncertain Linear State-Delayed Systems via Static Output Feedback

Abstract This paper examines the problem of robust stabilization via static output feedback for a class of uncertain linear state-delayed systems. Systems with a constant time-delay and subject to norm-bo~nded parameter uncertainty in the state matrices of the ʻcurrentʼ and ʻdelayedʼ states and in the input matnx are considered. We develop a method of robust stabilization based. on linear matrix inequalities. The proposed design method incorporates information on the size, or an upper-bound, of the time-delay. The case ofsystems with polytopic uncertainty is also discussed.

Robust Stabilization of Discrete-Time Multi-Model Systems Using Piecewise Affine State-Feedback

In this paper we develop a BMI based method for nonlinear robust stabilization. Robustness against model uncertainty is handled. The development is based on an uncertain multi-model representation of the plant, and an associated piecewise affine state-feedback structure. Assuming a quadratic Liapunov function, a BMI condition for robust (quadratic) stabilization is found. Control constraints are formulated as BMIs or LMIs. A branch-and-bound algorithm is used for solving the BMI problem, that is, finding the unknown quadratic Liapunov function and the piecewise affine state-feedback. Finally, an example is given.

Criteria for robust stability and stabilization of uncertain linear systems with state delay

This paper deals with the problem of robust stability analysis and robust stabilization for a class of uncertain linear systems with a time-varying state delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop delay-dependent methods for robust stability analysis and robust stabilization via linear memoryless state feedback. The proposed methods are given in terms of linear matrix inequalities.

Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach

This paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time-delay. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state-space model. We develop methods for robust stability analysis and robust stabilization. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities.

Robust Stabilization and H∞ Control of Uncertain Linear Time-Delay Systems

Abstract This paper examines the problems of robust stabilization and robust H ∞ control for linear systems with state delay and subject to norm-bounded parameter uncertainty. The case of a single, constant time-delay is considered and attention is focused on the design of memoryless state feedback controllers. We develop methods of robust stabilization and robust H ∞ control which depend on the size of the delay and are given in terms of linear matrix inequalities.

Teaching Stability and Robust Stability

Abstract The aim of this paper is to demonstrate that, in teaching stability theory for linear systems, there are two basic mathematical foundations which can be used: The principal of the argument and Lyapunov theory, according to the presentation of the system in the operator or time-domain, respectively. However, all stability criteria obtained using the characteristic polynomial can be proved using Lyapunov theory. Regarding robust stability, the easiest and most straightforward method is based on the principle of the argument and boundary crossing idea. It is shown that, almost all the robust stability results can be obtained in a simple way.

A method for robust stabilization

LetP(y,M) be a family of polynomials, depending on a controller parameter vector y in ℝ n+1, defined as follows: a family of interval matrices, and y in ℝ n+1, set Given an initial stabilizing controller y0, this paper provides a simple method to robustify y0, i.e., to obtain a controller parameter vector y1 which is more robust than y0. Furthermore we define the stability factort for a given robustly stable controller y, which serves as a measure of the robustness of y.

SMESによる電力系統のロバスト安定化制御法

SMESによる電力系統のロバスト安定化制御法

The Design of Robust Servo Systems Based on the Quadratic Stability Theory

The quadratic stability theory is known as a powerful method for robust stabilization of uncertain systems. This paper applies it to the tracking problem from the viewpoint of the inverse regulator problem and proposes a method of designing robust tracking controllers for linear systems with uncertain parameters. First, we solve the inverse problem of a quadratically stabilization problem. We then apply this result to Inverse LQ design theory and then give a criterion of choosing design parameters assuring quadratic stability of the closed system. Finally we show an example to illustrate the validity of the design method.