• 대한수학회보
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• 제43권1호
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• pp.149-159
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• 2006

This paper presents necessary and sufficient conditions for complete controllability, complete observability and realizability associated with matrix Lyapunov systems under certain smoothness conditions.

• 제어로봇시스템학회논문지
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• 제5권6호
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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.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.529-539
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• 2016

In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제4권1호
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• pp.1-6
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• 2004

This paper deals with a balanced model reduction for T-S(Takagi-Sugeno) fuzzy systems with time varying state delay. We define a generalized controllability gramian and a generalized observability gramian for a stable T-S fuzzy delayed systems. We obtain a balanced state space realization using the generalized controllability and observability gramian and obtain a reduced model by truncating states from the balanced state space realization. We also present an upper bound of the approximation error. The generalized controllability gramian and observability gramian can be computed from solutions of linear matrix inequalities. We demonstrate the efficacy of the suggested method by illustrating a numerical example.

• 전자공학회논문지 IE
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• 제44권3호
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• pp.51-55
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• 2007

본 논문에서는 선형 시변 시스템에 대하여 입력-상태, 입력-출력 변환을 적용하여 선형 시변 시스템의 가제어성과 가관측성을 해석하고자 한다. 또한 입력-상태, 입력-출력 변환을 통하여 얻어진, 변환된 시스템은 다중 적분기를 갖는 시스템으로 표현되며, 예제를 통하여 제안된 알고리즘을 확인하고, 검토하였다.

• 제어로봇시스템학회논문지
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• 제8권5호
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• pp.351-356
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• 2002

This papaer deals with a model reduction problem for linear systems with time varying parameters. For this problem, a controllability Grammian and an observability Grammian are introduced and computed by solving linear matrix inequalities. Using the controllability/observability Grammian, a balanced state space realization for linear parameter varying systems is obtained. From the balanced state space realization, a reduced model can be obtained by truncating not only states but also time varying parameters and an upper bound of the model reduction error is derived as well.

• 전자공학회논문지SC
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• 제40권5호
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• pp.326-332
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• 2003

본 연구에서는 상태변수에 시변 시간지연을 가진 선형시스템의 모델 차수축소를 취급한다. 이를 위하여 시간지연 시스템의 일반화 가제어성/가관측성 그래미안을 선형행렬 부등식의 해를 이용하여 정의하고 균형화된 상태공간 구현을 정의한다. 균형화된 상태공간 구현으로부터 상태변수론 절삭하여 차수축소된 시간지연 시스템을 구하고 모델 축소오차의 상한치를 제시한다. 수치예를 통하여 제시된 방법의 효용성을 입증한다.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1115-1125
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• 2023

This paper deals with the controllability of linear and nonlinear generalized fractional dynamical systems in finite dimensional spaces. The results are obtained by using fractional calculus, Mittag-Leffler function and Schauder's fixed point theorem. Observability of linear system is also discussed. Examples are given to illustrate the theory.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.73.6-73
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• 2001

In this paper, we consider a hierarchical decentralized supervisory control of discrete event systems underpartial observation in two-level hierarchical structure since the observability is a practical and general property in modeling of real systems. Hierarchical consistencies of controllability and observability on the hierarchical decentralized supervisory control are investigated and relevant conditions are proposed to ensure such hierarchical consistencies.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.557-567
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• 2006

This paper proves the invariability of reachable sets for the linear control system with positive isolated spectrum points in case where the principal operator generates $C_0-semigroup$ and derives the approximate controllability for the semilinear control system by using spectral operators with respect to isolated spectrum points.