We present a sufficient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We a...

We present a suucient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We als...

This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants...

This paper presents the adaptive control parameter identification of switched nonlinear system that uses model reference adaptive control (MRAC) method to track the variation of the state error to approach the ideal values. MRAC is treated as a class of switched nonlinear systems in which the unknown parameters appear linearly. At the same time, switched systems ensure the whole system stay sta...

prompt detection and diagnosis of faults in industrial systems areessential to minimize the production losses, increase the safety of the operatorand the equipment. several techniques are available in the literature to achievethese objectives. this paper presents fuzzy based control and fault detection for a6/4 switched reluctance motor. the fuzzy logic control performs like a classicalproporti...