• 제어로봇시스템학회논문지
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• 제13권11호
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• pp.1048-1052
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• 2007

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

• 제어로봇시스템학회논문지
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• 제22권6호
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• pp.397-402
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• 2016

This paper proposes a robust tracking control for constrained uncertain linear systems by combining a disturbance observer (DOB) and linear matrix inequality (LMI) based state feedback control. To this end, the state feedback control is designed for the nominal system and then a DOB based feed-forward control is added to reject uncertainties. In doing so, the DOB and state feedback controller are joined in a way that the combined control satisfies the input constraints and closed loop stability is guaranteed. Simulation results are provided to show that the proposed control scheme successfully stabilizes uncertain systems.

• Journal of Power Electronics
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• 제11권3호
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• pp.327-334
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• 2011

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.297-303
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• 2001

In this paper, the problem of the stability analysis for a class of linear neutral systems with time-varying delay is investigated. Using the Lyapunov method, a delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs) is presented. The LMIs can be easily solved by various convex optimization algorithms.

• 전자공학회논문지SC
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• 제39권6호
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• pp.20-26
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• 2002

본 논문에서는 시변 시간지연을 가지는 이산 선형 불확실성 시스템에 대한 보장 비용 제어문제를 다룬다. 본 논문에서 다루는 불확실성 시스템은 시변 노옴 한정 파라미터 불확실성을 가진다. 모든 허용 가능한 불확실성에 대해 폐루프 시스템이 자승적으로 안정하고 성능을 보장하는 제어기가 존재할 충분조건과 설계방법에 대해 논의한다. 또한, 변수 치환과 Schur 여수정리 등을 이용하여 충분조건을 모든 변수에 대한 선형 행렬 부등식(linear matrix inequality)으로 표현한다.

• 한국정밀공학회지
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• 제23권6호
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• pp.88-95
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• 2006

In this paper, the gain-scheduled control design proposed in the previous paper has been applied to a target tracking system. In such system, it is needed to attenuate disturbance effectively as long as control input satisfies the given constraint on its magnitude. The scheduled gains are derived in the framework of linear matrix inequality(LMI) optimization by means of the MatLab toolbox. Its effectiveness is verified along with the simulation results compared with the conventional optimum constant gain and the scheduled gain control with constant Q matrix cases.

• 제어로봇시스템학회논문지
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• 제11권11호
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• pp.895-900
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• 2005

We derive a linear matrix inequality(LMI) condition guaranteeing that any invariant zeros of a triple (A, B, C) lie in the open left half plane of the complex plane, i.e. $C(sI-A)^{-1}B$ is minimum phase. The LMI condition is equivalent to a certain constrained Lyapunov matrix equation which can be found in many results relating to stability analysis or control design. We show that the LMI condition can be used to simplify various control engineering problems such as a dynamic output feedback control problem, a variable structure static output feedback control problem, and a nonlinear system observer design problem. Finally, we give some numerical examples.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.513-522
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• 2006

This paper considers a robust output feedback $H\infty$ controller design method for singular systems with time-varying delay in state and parameter uncertainty in system matrix by an LMI approach and observer based technique, which can be solved efficiently by convex optimization. The sufficient condition for the existence of controller and the controller design method are presented by strict LMI(linear matrix inequality) approach. Since the obtained condition can be expressed as an LMI form, all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement and changes of variables.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.476-479
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• 2000

This paper deals with a robust pole placement method for uncertain linear systems. For all admissible uncertain parameters, a static output feedback controller is designed such that all the poles of the closed loop system are located within the prespecfied disk. It is shown that the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set guarantees the existence of the output feedback gain matrix for our control problem. By a sequence of convex optimization the aforementioned matrix is obtained. A numerical example is solved in order to illustrate efficacy of our design method.