A full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs

Stabilizability of Bimodal Piecewise Linear Systems with Continuous Vector Field

This paper studies the open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It turns out that this system class inherits the relationship be...

On the Controllability of Bimodal Piecewise Linear Systems

This paper studies controllability of bimodal systems that consist of two linear dynamics on each side of a given hyperplane. We show that the controllability properties of these systems can be inferred from those of linear systems for which the inputs are constrained in a certain way. Inspired by the earlier work on constrained controllability of linear systems, we derive necessary and suffici...

Design of robust fuzzy Sliding-Mode control for a class of the Takagi-Sugeno uncertain fuzzy systems using scalar Sign function

This article presents a fuzzy sliding-mode control scheme for a class of Takagi-Sugeno (T-S) fuzzy which are subject to norm-bounded uncertainties in each subsystem. The proposed stabilization method can be adopted to explore T-S uncertain fuzzy systems (TSUFS) with various local control inputs. Firstly, a new design is proposed to transform TSUFS into sliding-mode dynamic systems.In addi...

Piecewise Constant Controlled Linear Fuzzy Systems

Well-posed bimodal piecewise linear systems do not exhibit Zeno behavior

The phenomenon of infinitely mode transitions in a finite time interval is called Zeno behavior in hybrid systems literature. It plays a critical role in the study of numerical methods and fundamental system and control theoretic properties of hybrid systems. This paper studies Zeno behavior for bimodal piecewise linear systems with possibly discontinuous dynamics. Our treatment is inspired by ...