11,215 research outputs found
Stability of interconnected impulsive systems with and without time-delays using Lyapunov methods
In this paper we consider input-to-state stability (ISS) of impulsive control
systems with and without time-delays. We prove that if the time-delay system
possesses an exponential Lyapunov-Razumikhin function or an exponential
Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that
the average dwell-time condition is satisfied. Then, we consider large-scale
networks of impulsive systems with and without time-delays and we prove that
the whole network is uniformly ISS under a small-gain and a dwell-time
condition. Moreover, these theorems provide us with tools to construct a
Lyapunov function (for time-delay systems - a Lyapunov-Krasovskii functional or
a Lyapunov-Razumikhin function) and the corresponding gains of the whole
system, using the Lyapunov functions of the subsystems and the internal gains,
which are linear and satisfy the small-gain condition. We illustrate the
application of the main results on examples
Networked control systems in the presence of scheduling protocols and communication delays
This paper develops the time-delay approach to Networked Control Systems
(NCSs) in the presence of variable transmission delays, sampling intervals and
communication constraints. The system sensor nodes are supposed to be
distributed over a network. Due to communication constraints only one node
output is transmitted through the communication channel at once. The scheduling
of sensor information towards the controller is ruled by a weighted
Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the
existing results on NCSs in the presence of scheduling protocols (in the
frameworks of hybrid and discrete-time systems), we allow the communication
delays to be greater than the sampling intervals. A novel hybrid system model
for the closed-loop system is presented that contains {\it time-varying delays
in the continuous dynamics and in the reset conditions}. A new
Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov
functionals is introduced for the stability analysis of the delayed hybrid
systems. Polytopic type uncertainties in the system model can be easily
included in the analysis. The efficiency of the time-delay approach is
illustrated on the examples of uncertain cart-pendulum and of batch reactor
Decision algorithm for the stability of planar switching linear systems
This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not
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