Characterization of the $\mathcal{L}_2 $-Induced Norm for Linear Systems with Jumps with Applications to Sampled-Data Systems

Abstract

This paper considers a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the $\mathcal{L}_2 $-induced norm of a linear system with jumps is presented. Each iteration requires solving an algebraic Riccati equation. It is also shown that a linear feedback interconnection of a continuous-time finite-dimensional linear time-invariant (FDLTI) plant and a discrete-time finite-dimensional linear shift-invariant (FDLSI) controller can be represented as a linear system with jumps. This leads to an iterative method to compute the $\mathcal{L}_2 $-induced norm of a sampled-data system.