• Title, Summary, Keyword: linear time-varying system

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The robust control for a linear time-varying system using state transformation (상태 변환을 이용한 선형 시변 시스템에 대한 강건한 제어)

  • Cho, Do-Hyeoun;Lee, Sang-Hyo
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.1
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    • pp.1-9
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    • 1998
  • This paper is focussed on the problem of robustly stabilizing a transformable linear time-varying system. The considered system is a class of state feedback transformable linear systems. First, the real linear time-varying system is transformed into the linear time invariant system composed with the time-invariant linear part and the time-varying uncertainty part. Second, the solution to a quadratic stabilization problem in the transformed linear system is give via' Lyapunov methods. Then this solution is used to construct a stabilizing linear control law for the real linear time-varying system.

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Eigenvalue Assignment for Linear Time-Varying Systems via Ackermann-like Formula (선형 시변 시스템의 고유치 지정을 위한 Ackermann형 공식)

  • 이호철;최재원
    • Journal of Institute of Control, Robotics and Systems
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    • v.9 no.3
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    • pp.186-195
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    • 2003
  • This paper deals with eigenvalue assignment techniques for linear time-varying systems as a way of achieving feedback stabilization. For this, the novel eigenvalue concepts, which are the time-varying counterparts of the conventional (time-invariant) eigenvalue notions, are introduced. Then, the Ackermann-like formulae for SISO/MIMO linear time-varying systems are proposed. It is believed that these techniques are the generalized versions of the Ackermann formulae for linear time-invariant systems. The advantages of the proposed Ackermann-like formulae are that they neither require the transformation of the original system into the phase-variable form nor compute the eigenvalues of the original system. Two examples are given to demonstrate the capabilities of the proposed techniques.

Eigenstructure-Based Robust Stability Criterion for Linear Time-Varying Systems

  • Lee, Ho-Chul;Park, Jae-Weon
    • 제어로봇시스템학회:학술대회논문집
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    • pp.44.3-44
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    • 2002
  • Stability robustness of a linear time-varying system with time-varying structured state space uncertainties is considered by using extended-mean theorem and Bellman's lemma. The extended-mean theorem is a necessary and sufficient exponential stability criterion based on the recently developed PD-eigenvalue and PD-eigenvector for a linear time-varying system. Our new result required that the extended-mean of each nominal PD-eigenvalue should be negative real which is determined by a norm involving the structures of the uncertainty and the no...

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Robust Stability of Uncertain Discrete-Time Linear Systems with Time-Varying Delays (시변 시간 지연을 갖는 불확실한 이산 시간 선형 시스템의 견실 안정성)

  • Song, Seong-Ho;Park, Seop-Hyeong;Lee, Bong-Young
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.6
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    • pp.641-646
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    • 1999
  • This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

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A Frozen Time Receding Horizon Control for a Linear Discrete Time-Varying System (선형 이산 시변시스템을 위한 고정시간 이동구간 제어)

  • Oh, Myung-Hwan;Oh, Jun-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.16 no.2
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    • pp.140-144
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    • 2010
  • In the case of a linear time-varying system, it is difficult to apply the conventional stability conditions of RHC (Receding Horizon Control) to real physical systems because of computational complexity comes from time-varying system and backward Riccati equation. Therefore, in this study, a frozen time RHC for a linear discrete time-varying system is proposed. Since the proposed control law is obtained by time-invariant Riccati equation solved by forward iterations at each control time, its stability can be ensured by matrix inequality condition and the stability condition based on horizon for a time-invariant system, and they can be applied to real physical systems effectively in comparison with the conventional RHC.

Measures of modal and gross controllability/observability for linear time-varying systems (선형 시변 시스템에 대한 모드 및 총가제어성/가관측성 척도)

  • Choe, Jae-Won;Lee, Ho-Chul;Lee, Dal-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.6
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    • pp.647-655
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    • 1999
  • For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

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A New Gain Scheduled QFT Method Based on Neural Networks for Linear Time-Varying System (선형 시변시스템을 위한 신경망 기반의 새로운 이득계획 QFT 기법)

  • Park, Jae-Seon;Im, Ki-Hong
    • Journal of Institute of Control, Robotics and Systems
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    • v.6 no.9
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    • pp.758-767
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    • 2000
  • The properties of linear time-varying(LTV) systems vary because of the time-varying property of plant parameters. The generalized controller design method for linear time-varying systems does not exit because the analytic soultion of dynamic equation has not been found yet. Hence, to design a controller for LTV systems, the robust control methods for uncertain LTI systems which are the approximation of LTV systems have been generally ised omstead. However, these methods are not sufficient to reflect the fast dynamics of the original time-varying systems such as missiles and supersonic aircraft. In general, both the performance and the robustness of the control system which is designed with these are not satisfactory. In addition, since a better model will give the more robustness to the controlled system, a gain scheduling technique based on LTI controller design methods has been uesd to solve time problem. Therefore, we propose a new gain scheduled QFT method for LTV systems based on neural networks in this paper. The gain scheduled QFT involves gain dcheduling procedured which are the first trial for QFT and are well suited consideration of the properties of the existing QFT method. The proposed method is illustrated by a numerical example.

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Asymptotic Stability of Discrete Time Linear Systems with Time Varying Delays (시변시간지연을 갖는 이산시간 선형시스템의 점근안정도)

  • Song, Seong-Ho;Kim, Jeom-Keun;Kang, Chang-Ik
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.5
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    • pp.580-585
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    • 1999
  • This paper deals with the stability of discrete time linear systems with time varying delays in state. In this paper, the magnitude of time-varying delays is assumed to be upper-bouded. The stability of discrete time linear systems with time-varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

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Stabilizing Controller Design for Linear Time-Varying Systems Using Ackerman-like Formula

  • Choi, Jae-Weon;Lee, Ho-Chul
    • 제어로봇시스템학회:학술대회논문집
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    • pp.125.1-125
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    • 2001
  • This paper deals with the eigenvalue assignment technique for linear time-varying systems to achieve feedback stabilization. For this, we introduce the novel eigenvalue concepts. Then, we propose the Ackerman-like formula for linear time-varying systems. It is believed that this technique is the generalized version of the Ackerman formula forlinear time-invariant systems. The advantages of the proposed technique are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

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Variable Structure Controller for Linear Time-Varying Sampled-Data Systems with Disturbances (외란을 갖는 선형 시변 샘플링된 시스템에 대한 가변구조제어기)

  • Park Kang-Bak
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.51 no.12
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    • pp.556-561
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    • 2002
  • In this paper, a discrete-time variable structure controller for linear time-varying sampled-data systems with disturbances is proposed. The proposed method guarantees that the system state if globally uniformly ultimately bounded (G.U.U.B), and the ultimate bound is shown to be the order of T, O(T), where T is a sampling period.