Global exponential stability of switched systems

Abstract

This paper proposes a method for the stability analysis of deterministic switched systems. Two motivational examples are introduced (nonholonomic system and constrained pendulum). The finite collection of models consists of nonlinear models, and a switching sequence is arbitrary. It is supposed that there is no jump in the state at switching instants, and there is no Zeno behavior, i.e., there is a finite number of switches on every bounded interval. For the analysis of deterministic switched systems, the multiple Lyapunov functions are used, and the global exponential stability is proved. The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.

Robust Switching Control Systems with Input Delay

“…The supervisor (4) and (5), in this paper, is different in comparison with the supervisor described in [2] . Here, the main ingredient of supervisor is the index of performance of feedback control systems.…”

“…For example, the reference [3] presents a vision based cart-inverted pendulum system under a hybrid feedback configuration. In [4] was considered unicycle and constrained pendulum as examples for switched control systems. The reference [5] presents impedance control of a robot manipulator using hybrid control.…”

Some results of studies on the stability and controlability properties of the switched systems of differential equations

“…Unweighted matrices and nonnegative inequality approaches are used to arrive at less conservative stability results. Filipovic, in [22] proposes a method for the stability analysis of deterministic switched systems. The author introduces two examples of motivation (the unholonomic system and the limited pendulum).…”