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In this chapter, we shall deal with the stabilization problem for singular systems. The purpose is the design of controllers such that the closed-loop system is regular, stable and impulse-free (in the continuous case) or causal (in the discrete case). For continuous singular systems, both state feedback and dynamic output feedback controllers are considered. Based on the stability conditions presented in Chapter 2, the stabilizing controller design can be formulated as a convex optimization problem characterized by linear matrix inequalities (LMI). In the context of discrete singular systems, a necessary and sufficient condition for the existence of stabilizing state feedback controllers is obtained.
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