Solvability conditions and design for semi-global and global stabilization in the admissible set
In Chap. 7, we formulated two important problems, (1) the semi-global stabilization problem in the admissible set and (2) the global stabilization problem in the admissible set. Moreover, based on the structural properties of the mapping from the control input to the constrained output, a taxonomy of constraints was developed there. In view of such a taxonomy, this chapter concentrates on semi-global as well as global stabilization problems in the admissible set. The nature and solvability of these stabilization problems as well as appropriate design of controllers differ profoundly for the two different cases of right and non-right-invertible constraints. Because of this, we consider here these two cases separately. In particular, we consider the case of right-invertible and non-right-invertible constraints, respectively, in Sects. 8.2 and 8.3 for continuous-time systems. Similarly, we consider the same in Sects. 8.4 and 8.5 for discrete-time systems. This chapter is primarily based on our work by Saberi et al. ( Automatica 38(4):639654, 2002; International Journal on Robust & Non-linear Control 14(5):435461, 2004; International Journal on Robust & Nonlinear Control 14(13–14):1087-1103, 2004).
KeywordsState Feedback Global Stabilization Solvability Condition Algebraic Riccati Equation Measurement Feedback
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