LYAPUNOV STABILITY OF LINEAR CONTINUOUS SINGULAR SYSTEMS: AN OVERVIEW

In this article a detailed overview of Lyapunov stability of linear continuous systems is presented. The conditions for the existence of the solutions for both regular and irregular singular linear systems are introduced. To guarantee an asymptotical stability for linear continuous singular systems and to provide an impulse-free motion of the system, new stability conditions are analyzed. In the control theory it is sometimes of significant interest to preserve specific system properties under large perturbations of system models. Consequently, the insensitiveness of the system properties, so-called system robustness, is analyzed in details. Together with the system stability, the stability robustness problem is investigated. A considerable attention is focused on the design of controllers for multivariable linear systems so that certain system properties could be preserved under various classes of perturbations occurring in the system.

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