1,187 research outputs found
Relaxed ISS Small-Gain Theorems for Discrete-Time Systems
In this paper ISS small-gain theorems for discrete-time systems are stated,
which do not require input-to-state stability (ISS) of each subsystem. This
approach weakens conservatism in ISS small-gain theory, and for the class of
exponentially ISS systems we are able to prove that the proposed relaxed
small-gain theorems are non-conservative in a sense to be made precise. The
proofs of the small-gain theorems rely on the construction of a dissipative
finite-step ISS Lyapunov function which is introduced in this work.
Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of
ISS Lyapunov functions, are shown to be sufficient and necessary to conclude
ISS of the overall system.Comment: input-to-state stability, Lyapunov methods, small-gain conditions,
discrete-time non-linear systems, large-scale interconnection
Robust distributed linear programming
This paper presents a robust, distributed algorithm to solve general linear
programs. The algorithm design builds on the characterization of the solutions
of the linear program as saddle points of a modified Lagrangian function. We
show that the resulting continuous-time saddle-point algorithm is provably
correct but, in general, not distributed because of a global parameter
associated with the nonsmooth exact penalty function employed to encode the
inequality constraints of the linear program. This motivates the design of a
discontinuous saddle-point dynamics that, while enjoying the same convergence
guarantees, is fully distributed and scalable with the dimension of the
solution vector. We also characterize the robustness against disturbances and
link failures of the proposed dynamics. Specifically, we show that it is
integral-input-to-state stable but not input-to-state stable. The latter fact
is a consequence of a more general result, that we also establish, which states
that no algorithmic solution for linear programming is input-to-state stable
when uncertainty in the problem data affects the dynamics as a disturbance. Our
results allow us to establish the resilience of the proposed distributed
dynamics to disturbances of finite variation and recurrently disconnected
communication among the agents. Simulations in an optimal control application
illustrate the results
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
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