5,429 research outputs found
Balanced truncation for linear switched systems
In this paper, we present a theoretical analysis of the model reduction
algorithm for linear switched systems. This algorithm is a reminiscence of the
balanced truncation method for linear parameter varying systems. Specifically
in this paper, we provide a bound on the approximation error in L2 norm for
continuous-time and l2 norm for discrete-time linear switched systems. We
provide a system theoretic interpretation of grammians and their singular
values. Furthermore, we show that the performance of bal- anced truncation
depends only on the input-output map and not on the choice of the state-space
representation. For a class of stable discrete-time linear switched systems (so
called strongly stable systems), we define nice controllability and nice
observability grammians, which are genuinely related to reachability and
controllability of switched systems. In addition, we show that quadratic
stability and LMI estimates of the L2 and l2 gains depend only on the
input-output map.Comment: We have corrected a number of typos and inconsistencies. In addition,
we added new results in Theorem
Stability of uniformly bounded switched systems and Observability
This paper mainly deals with switched linear systems defined by a pair of
Hurwitz matrices that share a common but not strict quadratic Lyapunov
function. Its aim is to give sufficient conditions for such a system to be
GUAS.We show that this property of being GUAS is equivalent to the uniform
observability on of a bilinear system defined on a subspace whose
dimension is in most cases much smaller than the dimension of the switched
system.Some sufficient conditions of uniform asymptotic stability are then
deduced from the equivalence theorem, and illustrated by examples.The results
are partially extended to nonlinear analytic systems
Midpoint based balanced truncation for switched linear systems with known switching signal
We propose a novel model reduction approachfor switched linear systems with known switching signal. Theclass of considered systems encompasses switched systems withmode-dependent state-dimension as well as impulsive systems.Our method is based on a suitable definition of (time-varying)reachability and observability Gramians and we show that theseGramians satisfy precise interpretations in terms of input andoutput energy. Based on balancing the midpoint Gramians, wepropose a piecewise-constant projection based model reductionresulting in a switched linear system of smaller size
Observability of Switched Linear Systems in Continuous Time
We study continuous-time switched linear systems with unobserved and exogeneous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both autonomous and non-autonomous cases
Model Reduction by Moment Matching for Linear Switched Systems
Two moment-matching methods for model reduction of linear switched systems
(LSSs) are presented. The methods are similar to the Krylov subspace methods
used for moment matching for linear systems. The more general one of the two
methods, is based on the so called "nice selection" of some vectors in the
reachability or observability space of the LSS. The underlying theory is
closely related to the (partial) realization theory of LSSs. In this paper, the
connection of the methods to the realization theory of LSSs is provided, and
algorithms are developed for the purpose of model reduction. Conditions for
applicability of the methods for model reduction are stated and finally the
results are illustrated on numerical examples.Comment: Sent for publication in IEEE TAC, on October 201
Reduced realizations and model reduction for switched linear systems:a time-varying approach
In the last decades, switched systems gained much interest as a modeling framework in many applications. Due to a large number of subsystems and their high-dimensional dynamics, such systems result in high complexity and challenges. This motivates to find suitable reduction methods that produce simplified models which can be used in simulation and optimization instead of the original (large) system. In general, the study aims to find a reduced model for a given switched system with a fixed switching signal and known mode sequence. This thesis concerns first the reduced realization of switched systems with known mode sequence which has the same input-output behavior as original switched systems. It is conjectured that the proposed reduced system has the smallest order for almost all switching time duration. Secondly, a model reduction method is proposed for switched systems with known switching signals which provide a good model with suitable thresholds for the given switched system. The quantitative information for each mode is carried out by defining suitable Gramians and, these Gramians are exploited at the midpoint of the given switching time duration. Finally, balanced truncation leads to a modewise reduction. Later, a model reduction method for switched differential-algebraic equations in continuous time is proposed. Thereto, a switched linear system with jumps and impulses is constructed which has the identical input-output behavior as original systems. Finally, a model reduction approach for singular linear switched systems in discrete time is studied. The choice of initial/final values of the reachability and observability Gramians are also investigated
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