373 research outputs found
Strict Positive Realness of Descriptor Systems in State Space
In this paper we give necessary and sufficient
spectral conditions for various notions of strict positive realness
for single input single output, impulse free Descriptor Systems.
These conditions only require calculation of eigenvalues of a
single matrix. A characterization of a KYP-like lemma for
descriptor systems is also derived, and its implications for the
stability of a class of switched descriptor systems are briefly
discussed
Stability results for constrained dynamical systems
Differential-Algebraic Equations (DAE) provide an appropriate framework to model and
analyse dynamic systems with constraints. This framework facilitates modelling of the
system behaviour through natural physical variables of the system, while preserving the
topological constraints of the system. The main purpose of this dissertation is to investigate
stability properties of two important classes of DAEs. We consider some special cases of
Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of
Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus
on two properties: passivity and a generalization of passivity and small gain theorems called
mixed property. These properties play an important role in the control design of large-scale
interconnected systems. An important bottleneck for a design based on the aforementioned
properties is their verification. Hence we intend to develop easily verifiable conditions to
check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input
Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability
and this problem forms the basis for the second part of the thesis. In this part, we try
to find conditions under which there exists a common Lyapunov function for all modes
of the switched system, thus guaranteeing exponential stability of the switched system.
These results are primarily developed for continuous-time systems. However, simulation and
control design of a dynamic system requires a discrete-time representation of the system
that we are interested in. Thus, it is critical to establish whether discrete-time systems,
inherit fundamental properties of the continuous-time systems from which they are derived.
Hence, the third part of our thesis is dedicated to the problems of preserving passivity,
mixedness and Lyapunov stability under discretization. In this part, we examine several
existing discretization methods and find conditions under which they preserve the stability
properties discussed in the thesis
Stability results for constrained dynamical systems
Differential-Algebraic Equations (DAE) provide an appropriate framework to model and
analyse dynamic systems with constraints. This framework facilitates modelling of the
system behaviour through natural physical variables of the system, while preserving the
topological constraints of the system. The main purpose of this dissertation is to investigate
stability properties of two important classes of DAEs. We consider some special cases of
Linear Time Invariant (LTI) DAEs with control inputs and outputs, and also a special class of
Linear switched DAEs. In the first part of the thesis, we consider LTI systems, where we focus
on two properties: passivity and a generalization of passivity and small gain theorems called
mixed property. These properties play an important role in the control design of large-scale
interconnected systems. An important bottleneck for a design based on the aforementioned
properties is their verification. Hence we intend to develop easily verifiable conditions to
check passivity and mixedness of Single Input Single Output (SISO) and Multiple Input
Multiple Output (MIMO) DAEs. For linear switched DAEs, we focus on the Lyapunov stability
and this problem forms the basis for the second part of the thesis. In this part, we try
to find conditions under which there exists a common Lyapunov function for all modes
of the switched system, thus guaranteeing exponential stability of the switched system.
These results are primarily developed for continuous-time systems. However, simulation and
control design of a dynamic system requires a discrete-time representation of the system
that we are interested in. Thus, it is critical to establish whether discrete-time systems,
inherit fundamental properties of the continuous-time systems from which they are derived.
Hence, the third part of our thesis is dedicated to the problems of preserving passivity,
mixedness and Lyapunov stability under discretization. In this part, we examine several
existing discretization methods and find conditions under which they preserve the stability
properties discussed in the thesis
A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels
This paper presents an algorithm for checking and enforcing passivity of
behavioral reduced-order macromodels of LTI systems, whose frequency-domain
(scattering) responses depend on external parameters. Such models, which are
typically extracted from sampled input-output responses obtained from numerical
solution of first-principle physical models, usually expressed as Partial
Differential Equations, prove extremely useful in design flows, since they
allow optimization, what-if or sensitivity analyses, and design centering.
Starting from an implicit parameterization of both poles and residues of the
model, as resulting from well-known model identification schemes based on the
Generalized Sanathanan-Koerner iteration, we construct a parameter-dependent
Skew-Hamiltonian/Hamiltonian matrix pencil. The iterative extraction of purely
imaginary eigenvalues ot fhe pencil, combined with an adaptive sampling scheme
in the parameter space, is able to identify all regions in the
frequency-parameter plane where local passivity violations occur. Then, a
singular value perturbation scheme is setup to iteratively correct the model
coefficients, until all local passivity violations are eliminated. The final
result is a corrected model, which is uniformly passive throughout the
parameter range. Several numerical examples denomstrate the effectiveness of
the proposed approach.Comment: Submitted to the IEEE Transactions on Components, Packaging and
Manufacturing Technology on 13-Apr-201
Guaranteed passive parameterized macromodeling by using Sylvester state-space realizations
A novel state-space realization for parameterized macromodeling is proposed in this paper. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. This technique is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parameterized macromodels. The key points of the novel state-space realizations are the choice of a proper pivot matrix and a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester realization for parameterized macromodeling
Dissipativity Analysis of Descriptor Systems Using Image Space Characterization
In this paper, we analyze the dissipativity for descriptor systems with impulsive behavior based on image space analysis. First, a new image space is used to characterize state responses for descriptor systems. Based on such characterization and an integral property of delta function, a new necessary and sufficient condition for the dissipativity of descriptor systems is derived using the linear matrix inequality (LMI) approach. Also, some of the earlier related results on dissipativity for linear systems are investigated in the framework proposed in this paper. Finally, two examples are given to show the validity of the derived results
Passivity check of S-Parameter descriptor systems via S-Parameter generalized hamiltonian methods
This paper extends the generalized Hamiltonian method (GHM) (Zhang , 2009; Zhang and Wong, 2010) and its half-size variant (HGHM) (Zhang and Wong, 2010) to their S-parameter counterparts (called S-GHM and S-HGHM, respectively), for testing the passivity of S-parameter descriptor-form models widely used in high-speed circuit and electromagnetic simulations. The proposed methods are capable of accurately detecting the possible nonpassive regions of descriptor-form models with either scattering or hybrid (impedance or admittance) transfer matrices. Their effectiveness and accuracy are verified with several practical examples. The S-GHM and S-HGHM methods presented here provide a foundation for the passivity enforcement of - parameter descriptor systems. © 2006 IEEE.published_or_final_versio
New impulse (noncausality) test for descriptor systems by Mobius-transformation
Descriptor systems (DSs) are usually used to model very-large-scale integration (VLSI) circuit systems and multibody dynamics macromodeling. The analysis of DSs, however, is much more complicated than linear time-invariant (LTI) systems due to the poles at infinity. Mȯbius transformation (MT) provides a way to transform poles at infinity to finite poles and largely facilitates the reuse or adaptation of the standard techniques for LTI system to analyze DSs. Nonetheless, MT is well known in the literature and its potential use is currently less appreciated in the analysis of DSs. This paper gives a new way to the impulse (noncausality) test using the properties of the transformed LTI systems by MT. Moreover, the applications to the analysis of controllability, observability and regularity are given. Numerical examples are included to show the effectiveness of the proposed method. © 2012 Chinese Assoc of Automati.published_or_final_versio
- …