12 research outputs found
Switching and stability properties of conewise linear systems
Being a unique phenomenon in hybrid systems, mode switch
is of fundamental importance in dynamic and control analysis. In
this paper, we focus on global long-time switching and stability
properties of conewise linear systems (CLSs), which are a class of
linear hybrid systems subject to state-triggered switchings
recently introduced for modeling piecewise linear systems. By
exploiting the conic subdivision structure, the “simple switching
behavior” of the CLSs is proved. The infinite-time mode switching
behavior of the CLSs is shown to be critically dependent on two
attracting cones associated with each mode; fundamental properties
of such cones are investigated. Verifiable necessary and
sufficient conditions are derived for the CLSs with infinite mode
switches. Switch-free CLSs are also characterized by exploring
the polyhedral structure and the global dynamical properties. The
equivalence of asymptotic and exponential stability of the CLSs is
established via the uniform asymptotic stability of the CLSs that
in turn is proved by the continuous solution dependence on initial
conditions. Finally, necessary and sufficient stability conditions
are obtained for switch-free CLSs
Real-time estimation of the switching signal for perturbed switched linear systems
International audienceWe extend previous works of Fliess et al. [2008] on the estimation of the switching signal and of the state for switching linear systems to the perturbed case when the perturbation is structured that is when the perturbation is unknown but known to satisfy a certain differential equation (for example if the perturbation is constant then its time-derivative is zero). We characterize also singular inputs and/or perturbations for which the switched systems become undistinguishable. Several convincing numerical experiments are illustrating our techniques which are easily implementable
Graph Theoretic Analysis of Multi-Agent system Structural Properties
Ph.DDOCTOR OF PHILOSOPH
Review on computational methods for Lyapunov functions
Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function