Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1193.34014
de la Sen, M.; Ibeas, A.
Stability results of a class of hybrid systems under switched continuous-time and discrete-time control. (English)
[J] Discrete Dyn. Nat. Soc. 2009, Article ID 315713, 28 p. (2009). ISSN 1026-0226; ISSN 1607-887X/e

This paper addresses the stability problem for a switched system formed by a finite family of linear subsystems $$\dot x= A_ix+ B_iu\quad (i= 1,\dots, N),\quad x\in\bbfR^n,\ u\in\bbfR^m.$$ The authors assume that for each $i$, there exists a stabilizing linear feedback $u= K_ix$ for the $i$th subsystem, and that the resulting family of closed-loop subsystems admits a common quadratic Lyapunov function. The control law for the switched system is defined by means of a sequence of switching times $\tau_0= 0<\tau_1<\tau_2<\cdots$\ . On each interval $[\tau_j, \tau_{j+1})$ the control law may be indifferently defined as either $u(t)= K_ix(t)$ (where $i$ is the active index for the $j$th interval) or the sampled value $u(t)\equiv K_i x(\tau_j)$. The authors prove that asymptotic stability is guaranteed provided that the mesh size $\max\{\tau_{j+1}- \tau_j\}$ is sufficiently small. The paper contains also a sufficient condition for the existence of a common Lyapunov function, and extensions of the result to systems with static output feedback and/or centralized/decentralized control.
[Andrea Bacciotti (Torino)]

MSC 2000:: *34A36 Discontinuous equations
34D20 Lyapunov stability of ODE
34H05 ODE in connection with control problems
34H15

Keywords: switched systems; sampled data control; Lyapunov functions

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]