This chapter studies the stabilization of time-varying nonlinear uncertain type I systems. Firstly, two motivating examples are presented in order to introduce the so-called type I systems. By definition, a type I system is composed of a sub-FAS and an unforced stable subsystem. Secondly, the robust problem formulation for the uncertain type I system is proposed. That is to find a full-state feedback controller such that the uncertain type I system is robustly globally uniformly asymptotically stabilized. Thirdly, the relation between the robust input-to-state stabilization and the robust stabilization, of the uncertain type I system, is firstly discussed. Then robust stabilization with full state feedback is proposed for the uncertain type I system, which includes both cases of single-order FASs and multi-order FASs. Fourthly, the further issues about robust stabilization with partial state feedback are addressed, including the case of perturbed \(B(\cdot )\) matrix and robust control of FASs. Finally, two illustrative examples of full state feedback and partial state feedback are carried out to demonstrate the effect of the proposed approaches.

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Robust Stabilization of Type I Systems

  • Guang-Ren Duan

摘要

This chapter studies the stabilization of time-varying nonlinear uncertain type I systems. Firstly, two motivating examples are presented in order to introduce the so-called type I systems. By definition, a type I system is composed of a sub-FAS and an unforced stable subsystem. Secondly, the robust problem formulation for the uncertain type I system is proposed. That is to find a full-state feedback controller such that the uncertain type I system is robustly globally uniformly asymptotically stabilized. Thirdly, the relation between the robust input-to-state stabilization and the robust stabilization, of the uncertain type I system, is firstly discussed. Then robust stabilization with full state feedback is proposed for the uncertain type I system, which includes both cases of single-order FASs and multi-order FASs. Fourthly, the further issues about robust stabilization with partial state feedback are addressed, including the case of perturbed \(B(\cdot )\) matrix and robust control of FASs. Finally, two illustrative examples of full state feedback and partial state feedback are carried out to demonstrate the effect of the proposed approaches.