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 H∞H_{\infty}-Optimal Control Of Coupled ODE-PDE Systems

In this paper, we present a convex formulation of $H_{\infty}$-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 $H_{\infty}$ 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 $H_{\infty}$ 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 $H_{\infty}$-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 $H_{\infty}$-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