The paper deals with generalized linear systems, i.e. with systems of the form \(\dot x=Fx+Gu\), \(y=hx+J_0u+J_1\dot x +\ldots + J_{\nu}u^{(\nu)}\), where \(x\in\mathbb{R}^n\), \(u,\dot u,\ldots, u^{(\nu)}\in\mathbb{R}^m\) and \(y\in\mathbb{R}^p\) and \(F,G,H,J_0,\ldots,J_{\nu}\) matrices of appropriate size. Clearly \(u^{(k)}\) denotes the \(k\)-th time derivative of the input function and the above representation differs from the more common representation where \(J_1= \cdots = J_{\nu}=0\). In this way the class of generalized linear systems includes the so-called (regular) descriptor systems or singular systems \(E\dot x=Ax+Bu\), \(y=Cx+Du\), where \(E\) is an \((n,n)\)-matrix which is not necessarily nonsingular. The methods used in the paper stem from module theory and enable the author to study controllability, observability and the observer design problem for a generalized system.