Simultaneous stabilization by static output feedback: a rank-constrained LMI approach

Kim, Seog-Joo; Moon, Young-Hyun; Kwon, Seong-Geun

doi:10.1109/cdc.2006.376683

Cited by 9 publications

(5 citation statements)

References 16 publications

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“…Remark 4: Several applicable algorithms and methods such as given procedures in Kim and Moon (2006), Kim et al (2006), Orsi et al (2006) and Sun and Dai (2017), are presented by researchers to solve the rank-constrained optimization problems (RCOPs), that which are useable to solve the above RCOP.…”

Section: Design a Stabilizing 2-d Dynamic Output Feedback Controller Via Lmi Approachmentioning

confidence: 99%

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Asl

Madady

2021

Transactions of the Institute of Measurement and Control

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This paper investigates the asymptotic stabilization of the 2-D continuous-discrete-time systems via dynamic output feedback. The problem is formulated in a general framework, where the system and controller are both described by the Roesser model. By rigorous mathematical works, a linear matrix inequality (LMI) condition is established to ensure the asymptotic stability of the closed-loop system. Using this LMI condition, the problem of determining the stabilizing controller parameters is converted to a rank minimization problem (RMP) with an LMI constraint, or equivalently to a rank-constrained optimization problem (RCOP). When this RMP (or equivalently this RCOP) has a solution, then the controller parameters are obtained uniquely by an explicit formula in terms of this solution. Moreover, it is shown that one can transform the problem of one-dimensional continuous-time iterative learning control (ILC) design to a 2-D stabilization problem, and consequently solve it using the presented two-dimensional scheme. Some numerical examples are given to illustrate the proposed method.

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Section: Design a Stabilizing 2-d Dynamic Output Feedback Controller Via Lmi Approachmentioning

confidence: 99%

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Asl

Madady

2021

Transactions of the Institute of Measurement and Control

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“…The common control design is an indispensable step that should be checked before proceeding to switching. The common control design has a long history (see [2][3][4][5][6][7][8][9][10][11]) and several applications; indicatively, see [9][10][11], where the case of robot manipulators was studied. In the framework of the present common design requirement, studied for the class of multi-model normal linear time-invariant systems, the set of the outputs of each model of the multi-model system is divided into two subsets.…”

Section: Introductionmentioning

confidence: 99%

Common Noninteracting Control with Simultaneous Common Partial Zeroing with Application to a Tracked UGV

Koumboulis

Kouvakas

2023

Machines

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In several MIMO system applications, the deviations of some output performance variables from their nominal values are required to be controlled independently, while the other performance variables are required to remain at their nominal value. This problem, named noninteracting control with simultaneous partial output zeroing, is important in the case of the common design of multi-model systems. To this end, the problem of a common noninteracting control with simultaneous common partial output zeroing is formulated. The present paper aims to develop a solution to the problem of multi-model normal linear time-invariant systems via regular and static measurement output feedback. The present approach follows the method developed for the solution of the common I/O decoupling problem. The main results of the paper are the introduction and the formulation of the problem at hand, the establishment of the necessary and sufficient conditions for its solvability, and the derivation of the respective general solution of the controller matrices. For the resulting closed-loop system, the additional design requirement of approximate command following a simultaneous I/O stabilizability is studied using a composite norm 2 type cost function and a metaheuristic algorithm for the derivation of the free parameters of the controller. The present results are illustrated through a numerical example of a nonlinear process with two operating points. Moreover, all the above results are successfully applied to the two-model description of a robot-tracked UGV, using a common controller feeding back measurements of the motor currents and the orientation of the vehicle.

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“…It is worth pointing out that the simultaneous stabilization problem of the normal state-space system is introduced in 1982. Abundant results of simultaneous stabilization have been obtained in recent years [2][3][4][5][6]. In [2], several simultaneous external and internal stabilization problems have been considered under appropriate adaptive low-and-high gain feedback controllers.…”

Section: Introductionmentioning

confidence: 99%

“…In [2], several simultaneous external and internal stabilization problems have been considered under appropriate adaptive low-and-high gain feedback controllers. Simultaneous stabilization of linear systems has been solved by the static output feedback in [3]. In [4], the simultaneous stabilization of the multiinput-multioutput system has been investigated to develop a stabilizing controller.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Simultaneous Stabilization of a Set of Nonlinear Singular Systems

Sun

2021

Mathematical Problems in Engineering

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This study addresses the problems of finite-time simultaneous stabilization for two nonlinear singular systems and more than two nonlinear singular systems. First, we design a suitable output feedback controller and combine the two nonlinear singular systems to generate an augmented system by using an augmented technique. Based on a sufficient condition of the augmented system impulse-free, an important result, that is, the augmented system is finite-time stabilization is presented. Then, the finite-time stabilization problem of more than two singular systems is investigated by dividing the N systems into two sets. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed finite-time stabilization controller for two nonlinear singular systems.

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Simultaneous stabilization by static output feedback: a rank-constrained LMI approach

Cited by 9 publications

References 16 publications

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Common Noninteracting Control with Simultaneous Common Partial Zeroing with Application to a Tracked UGV

Finite-Time Simultaneous Stabilization of a Set of Nonlinear Singular Systems

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