Transformation of time-varying implicit linear systems of their Weierstrass canonical form (Q1202263)

The author considers the time-varying implicit system: \[ E(t)\dot x(t)=A(t)x(t)+B(t)u(t),\quad y(t)=C(t)x(t),\tag{1} \] where \(x(t)\in\mathbb{R}^ n\) is the semistate vector, \(u(t)\in\mathbb{R}^ m\) the input vector, \(y(t)\in\mathbb{R}^ p\) the output vector and \(E(t)\), \(A(t)\), \(B(t)\), \(C(t)\) real matrices with entries depending on time \(t\). He establishes necessary and sufficient conditions under which the system (1) can be transformed to its Weierstrass canonical form. Finally, an example that illustrates the transformation procedure is given.