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Controllability, Observability and Stabilization of a Class of Matrix Linear Systems

Bin Zhou, Guang‐Ren Duan, Zheng Zhong

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Abstract

In this paper we consider the controllability and observability properties of the matrix linear system X = AX +X d + BU,Y = CX where A,srf,B and C are some known matrices. It is shown that such system is controllable and observable if and only if the corresponding linear system X = AX + BU,Y = CX is controllable and observable, respectively. Some explicit conditions are established. Furthermore, stabilization of such matrix linear system by state feedback is considered.

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What this paper is about

In this paper we consider the controllability and observability properties of the matrix linear system X = AX +X d + BU,Y = CX where A,srf,B and C are some known matrices. It is shown that such system is controllable and observable if and only if the corresponding linear system X = AX + BU,Y = CX is controllable and observable, respectively. Some explicit conditions are established. Furthermore, stabilization of such matrix linear system by state feedback is considered.

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Available abstract

In this paper we consider the controllability and observability properties of the matrix linear system X = AX +X d + BU,Y = CX where A,srf,B and C are some known matrices. It is shown that such system is controllable and observable if and only if the corresponding linear system X = AX + BU,Y = CX is controllable and observable, respectively. Some explicit conditions are established. Furthermore, stabilization of such matrix linear system by state feedback is considered.

Key concepts: Observability, Controllability, Observable, Linear system, Matrix (chemical analysis), Control theory (sociology), Class (philosophy), Mathematics

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