Worst Case Performance Analysis of Linear Systems with Jumps with Applications to Sampled-Data Systems

In this paper, we consider a continuous-time linear system with finite jumps at discrete instants of time. An iterative method to compute the L
2
-induced norm of a linear system with jumps is presented. Each iteration requires solving an algebraic Riccati equation. We also show 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 L
2
-induced norm of a sampled-data system.