10,812 research outputs found
μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time
In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results
Stability analysis of a general class of singularly perturbed linear hybrid systems
Motivated by a real problem in steel production, we introduce and analyze a
general class of singularly perturbed linear hybrid systems with both switches
and impulses, in which the slow or fast nature of the variables can be
mode-dependent. This means that, at switching instants, some of the slow
variables can become fast and vice-versa. Firstly, we show that using a
mode-dependent variable reordering we can rewrite this class of systems in a
form in which the variables preserve their nature over time. Secondly, we
establish, through singular perturbation techniques, an upper bound on the
minimum dwell-time ensuring the overall system's stability. Remarkably, this
bound is the sum of two terms. The first term corresponds to an upper bound on
the minimum dwell-time ensuring the stability of the reduced order linear
hybrid system describing the slow dynamics. The order of magnitude of the
second term is determined by that of the parameter defining the ratio between
the two time-scales of the singularly perturbed system. We show that the
proposed framework can also take into account the change of dimension of the
state vector at switching instants. Numerical illustrations complete our study
Robust output stabilization: improving performance via supervisory control
We analyze robust stability, in an input-output sense, of switched stable
systems. The primary goal (and contribution) of this paper is to design
switching strategies to guarantee that input-output stable systems remain so
under switching. We propose two types of {\em supervisors}: dwell-time and
hysteresis based. While our results are stated as tools of analysis they serve
a clear purpose in design: to improve performance. In that respect, we
illustrate the utility of our findings by concisely addressing a problem of
observer design for Lur'e-type systems; in particular, we design a hybrid
observer that ensures ``fast'' convergence with ``low'' overshoots. As a second
application of our main results we use hybrid control in the context of
synchronization of chaotic oscillators with the goal of reducing control
effort; an originality of the hybrid control in this context with respect to
other contributions in the area is that it exploits the structure and chaotic
behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA
Distributed Consensus of Linear Multi-Agent Systems with Switching Directed Topologies
This paper addresses the distributed consensus problem for a linear
multi-agent system with switching directed communication topologies. By
appropriately introducing a linear transformation, the consensus problem is
equivalently converted to a stabilization problem for a class of switched
linear systems. Some sufficient consensus conditions are then derived by using
tools from the matrix theory and stability analysis of switched systems. It is
proved that consensus in such a multi-agent system can be ensured if each agent
is stabilizable and each possible directed topology contains a directed
spanning tree. Finally, a numerical simulation is given for illustration.Comment: The paper will be presented at the 2014 Australian Control Conference
(AUCC 2014), Canberra, Australi
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