183 research outputs found
A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
In this paper, we consider input-output properties of linear systems
consisting of PDEs on a finite domain coupled with ODEs through the boundary
conditions of the PDE. This framework can be used to represent e.g. a lumped
mass fixed to a beam or a system with delay. This work generalizes the
sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a
recently developed concept of fundamental state and the associated
boundary-condition-free representation. The conditions of the generalized KYP
are tested using the PQRS positive matrix parameterization of operators
resulting in a finite-dimensional LMI, feasibility of which implies prima facie
provable passivity or L2-gain of the system. No discretization or approximation
is involved at any step and we use numerical examples to demonstrate that the
bounds obtained are not conservative in any significant sense and that
computational complexity is lower than existing methods involving
finite-dimensional projection of PDEs
Duality and -Optimal Control Of Coupled ODE-PDE Systems
In this paper, we present a convex formulation of -optimal
control problem for coupled linear ODE-PDE systems with one spatial dimension.
First, we reformulate the coupled ODE-PDE system as a Partial Integral Equation
(PIE) system and show that stability and performance of the PIE
system implies that of the ODE-PDE system. We then construct a dual PIE system
and show that asymptotic stability and performance of the dual
system is equivalent to that of the primal PIE system. Next, we pose a convex
dual formulation of the stability and -performance problems using
the Linear PI Inequality (LPI) framework. LPIs are a generalization of LMIs to
Partial Integral (PI) operators and can be solved using PIETOOLS, a MATLAB
toolbox. Next, we use our duality results to formulate the stabilization and
-optimal state-feedback control problems as LPIs. Finally, we
illustrate the accuracy and scalability of the algorithms by constructing
controllers for several numerical examples
Placing the RPL32 Promoter Upstream of a Second Promoter Results in a Strongly Increased Number of Stably Transfected Mammalian Cell Lines That Display High Protein Expression Levels
The use of high stringency selection systems commonly results in a strongly diminished number of stably transfected mammalian cell lines. Here we placed twelve different promoters upstream of an adjacent primary promoter and tested whether this might result in an increased number of colonies; this is in the context of a stringent selection system. We found that only the promoter of the human ribosomal protein, RPL32, induced a high number of colonies in CHO-DG44 cells. This phenomenon was observed when the RPL32 promoter was combined with the CMV, SV40, EF1-α, and the β-actin promoters. In addition, these colonies displayed high protein expression levels. The RPL32 promoter had to be functionally intact, since the deletion of a small region upstream of the transcription start site demolished its positive action. We conclude that adding the RPL32 promoter to an expression cassette in cis may be a powerful tool to augment gene expression levels
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