Abstract:
This paper considers a linear continuous-discrete time-varying system described by a set of differential and difference equations on a finite horizon. For such a hybrid system, the concept of the generalized $\mathcal{H}_2$ norm is introduced, representing the induced norm of a linear operator generated by the system under consideration. This norm is characterized in terms of Lyapunov difference equations and also in terms of recursive linear matrix inequalities. Discrete time-varying optimal controllers, including multiobjective ones, that minimize the generalized $\mathcal{H}_2$ norm of the closed loop system are designed.
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