Hybrid State Feedback Stabilization with l2
Performance for Discrete-Time Switched Linear
Hai Lin and Panos J. Antsaklis
In this paper, the co-design of continuous-variable controllers and discrete-event switching logics, both in state
feedback form, is investigated for a class of discrete-time switched linear control systems. It is assumed that none
of the subsystems is stabilized through a continuous state feedback alone. However, it is possible to stabilize the
whole switched system via carefully designing both the continuous controllers and the switching logics. Sufficient
synthesis conditions for this co-design problem are proposed here in the form of bilinear matrix inequalities, which
is based on the argument of multiple Lyapunov functions. The closed-loop switched system forms a special class
of linear hybrid system, and is shown to be asymptotically stable with a finite l2 induced gain.
Switched systems, controller synthesis, l2 induced gain, Lyapunov methods.
A remarkable feature of a switched system is that even when all its subsystems are unstable it is still possible
to be stabilized by properly designed switching laws , . As one of the benchmark problems , , the
synthesis of stabilizing switching signals for a given collection of dynamical systems, especially linear systems,
has attracted a lot of attentions recently; see for example the survey papers , , , , , the recent