Controllability and observability of time-invariant linear dynamic systems.
The paper is concerned with linear dynamic time-invariant control systems of the forms NEWLINE\[NEWLINEx^{\Delta }(t)=-Ax^{\sigma }(t)+Bu(t),\;\;\;y(t)=Cx^{\sigma }(t),\tag{1}NEWLINE\]NEWLINE where \(x\), \(y\), \(u\) denote the state, input, and output of the system, respectively. It is assumed that \(u\) is an rd-continuous function, and \(A\) is a regressive matrix.NEWLINENEWLINEThe authors derive necessary and sufficient conditions for the controllability and reachability of system (1), which generalize the usual ones which are well known in the classical control theory.NEWLINENEWLINEThe final result is a duality theorem, which says that the controllability of (1) is equivalent to the observability of NEWLINE\[NEWLINEx^{\Delta }(t)=A^T x(t)+C^T u(t),\;\;\;y(t)=B^T x(t).NEWLINE\]
scientific article; zbMATH DE number 6092234