Sufficient conditions for stability of linear time-varying systems
The paper is concerned with the exponential stability of the n- dimensional system \(\dot x(t)=A(t)x(t),\) \(t\geq 0\), where A(t) is a piecewise continuous matrix function with \(\| A(t)\| \leq M\) and \(\sigma (A(t))\subset \{s\in {\mathbb{C}}| Re(s)<-\alpha \}\) for all \(t\geq 0\) and some constants \(\alpha\), \(M\geq 0\). Based on the a priori knowledge of M and \(\alpha\) explicit formulae which guarantee the exponential stability of the system are given.
scientific article; zbMATH DE number 4065469