Stability and Stabilizability

This chapter is devoted to the study of the stability and the stabilizability of linear time invariant systems with time delay using the Lyapunov method and linear matrix inequality (see Appendix A). For this purpose, let us consider the following linear continuous-time system with time delay: $$ \left\{ \begin{gathered} \dot x(t) = Ax(t) + \Sigma _{j = 1}^mx(t - {\tau _j}) + Bu(t) \hfill \\ y(t) = Cx(t) \hfill \\ x(t) = \phi (t),\;t \in [ - \overline \tau ,0), \hfill \\ \end{gathered} \right. $$ (3.1)