Switching Stabilizability for Continuous-Time Uncertain Switched Linear Systems

Abstract

Abstract-This paper investigates the switching stabilizability problem for a class of continuous-time switched linear systems with time-variant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closed-loop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuous-time uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only.

Discrete robust switched H∞ tracking state feedback controllers for lateral vehicle control

“…Particularly, stability and stabilization problems of switched continuous-time and discrete-time linear systems were addressed in Narendra and Balakrishnan (1994), Liberzon and Morse (1999), Sun and Ge (2005), Lin and Antsaklis (2007), Lin and Antsaklis (2009), Branicky (1998), Daafouz et al (2002), Koenig et al (2008) and Du, Jiang, Shi, and Zhou (2007). The stability of other switched systems was also investigated such as switched linear and nonlinear descriptor systems (Koenig et al, 2008;Koenig & Marx, 2009), switched discrete-time systems with constant and timevarying delays (Du et al, 2007;Wu & Zheng, 2009), and recently switched linear systems with singular perturbation (Deaecto, Daafouz, & Geromel, 2012;Hachemi, Sigalotti, & Daafouz, 2012).…”

On infinity norms as Lyapunov functions for piecewise affine systems

“…Unfortunately, neither of the above procedures translates to PWA systems straightforwardly. To the best of the authors' knowledge, the existing results for hybrid systems consist of: stability analysis of continuoustime PWA systems via piecewise linear Lyapunov functions [2], switching stabilizability for continuous-time switched linear systems via polyhedral-like Lyapunov functions [23] and, synthesis of stabilizing state-feedback control laws for discrete-time PWA systems via nonlinear programming [24,25]. In this context it is worth to mention also the on-line synthesis method based on linear programming and trajectory-dependent Lyapunov functions, proposed recently in [26], which can be used to stabilize the closed-loop trajectory of a PWA system for a given initial condition.…”

Asymptotic Disturbance Attenuation Properties for Continuous-Time Uncertain Switched Linear Systems

“…The last decade has seen increasing research activities in the field of switched systems, and the main efforts typically focus on the analysis of dynamic behaviors, such as stability, controllability, reachability, and observability etc., and aim to design controllers with guaranteed stability and optimized performance, see e.g., Liberzon et al [1999], Decarlo et al [2000], Hespanha [2003], Sun et al [2005], Lin et al [2005Lin et al [ , 2007. However, the literature on robust performance of switched systems is still relatively sparse, and most existing results assume that the disturbances are constrained to have finite energy, i.e., bounded L 2 norm, see e.g.…”