4,318 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
Integral Input-to-State Stability of Nonlinear Time-Delay Systems with Delay-Dependent Impulse Effects
This paper studies integral input-to-state stability (iISS) of nonlinear
impulsive systems with time-delay in both the continuous dynamics and the
impulses. Several iISS results are established by using the method of
Lyapunov-Krasovskii functionals. For impulsive systems with iISS continuous
dynamics and destabilizing impulses, we derive two iISS criteria that guarantee
the uniform iISS of the whole system provided that the time period between two
successive impulse moments is appropriately bounded from below. Then we provide
an iISS result for systems with unstable continuous dynamics and stabilizing
impulses. For this scenario, it is shown that the iISS properties are
guaranteed if the impulses occur frequently enough. For impulsive systems with
stabilizing impulses and stable continuous dynamics for zero input, we obtain
an iISS result which shows that the entire system is uniformly iISS over
arbitrary impulse time sequences. As applications, iISS properties of a class
of bilinear systems are studied in details with simulations to demonstrate the
presented results
Minimal data rate stabilization of nonlinear systems over networks with large delays
Control systems over networks with a finite data rate can be conveniently
modeled as hybrid (impulsive) systems. For the class of nonlinear systems in
feedfoward form, we design a hybrid controller which guarantees stability, in
spite of the measurement noise due to the quantization, and of an arbitrarily
large delay which affects the communication channel. The rate at which feedback
packets are transmitted from the sensors to the actuators is shown to be
arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde
Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany
Mathematical control of complex systems 2013
Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)
On the existence and exponential attractivity of a unique positive almost periodic solution to an impulsive hematopoiesis model with delays
In this paper, a generalized model of hematopoiesis with delays and impulses
is considered. By employing the contraction mapping principle and a novel type
of impulsive delay inequality, we prove the existence of a unique positive
almost periodic solution of the model. It is also proved that, under the
proposed conditions in this paper, the unique positive almost periodic solution
is globally exponentially attractive. A numerical example is given to
illustrate the effectiveness of the obtained results.Comment: Accepted for publication in AM
A looped-functional approach for robust stability analysis of linear impulsive systems
A new functional-based approach is developed for the stability analysis of
linear impulsive systems. The new method, which introduces looped-functionals,
considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid
of exponential terms. This allows one to easily formulate dwell-times results,
for both certain and uncertain systems. It is also shown that this approach may
be applied to a wider class of impulsive systems than existing methods. Some
examples, notably on sampled-data systems, illustrate the efficiency of the
approach.Comment: 13 pages, 2 figures, Accepted at Systems & Control Letter
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
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