# Antonis

## Contents

## Publications

### Thesis

[1] A. Papachristodoulou. Scalable Analysis of Nonlinear Systems Using Convex Optimization. PhD Thesis, California Institute of Technology, Pasadena CA, 2005. PDF

### Systems Biology

[2] H. El-Samad, S. Prajna, A. Papachristodoulou, J. C. Doyle, and M. Khammash. Advanced Methods and Algorithms for Biological Networks Analysis. Proceedings of the IEEE, 94(4): 832–853, 2006.

[3] A. Papachristodoulou and B. Recht. Determining Interconnections in Chemical Reaction Networks. In Proceedings of the American Control Conference, 2007.

[4] A. Papachristodoulou and H. El-Samad. Distinguishing between Biochemical Network Models. In Proceedings of the American Control Conference, 2007.

[5] H. El-Samad, M. Fazel, X. Liu, A. Papachristodoulou, S. Prajna. Stochastic Reachability Analysis in Complex Biological Networks. In Proceedings of the American Control Conference, 2006.

[6] T.-M. Yi, M. Fazel, X. Liu, O. Otitoju, J. Gonçalves, A. Papachristodoulou, S. Prajna, J. C. Doyle. Application of Robust Model Validation Using SOSTOOLS to the Study of G-Protein Signaling in Yeast. In Proceedings of Foundations of Systems Biology in Engineering, 2005.

[7] H. El-Samad, S. Prajna, A. Papachristodoulou, M. Khammash, and J.C. Doyle. Model invalidation and robustness analysis of the bacterial heat shock response using SOSTOOLS. In Proceedings of the IEEE Conference on Decision and Control, 2003.

### Large-Scale Systems Analysis and Design

[8] A. Papachristodoulou, L. Li and J. C. Doyle. Methodological Frameworks for Large-scale Network Analysis and Design. ACM SIGCOMM Computer Communications Review, 34(3): 7 – 20, 2004.

[9] A. Papachristodoulou and A. Jadbabaie. Effects of Delay on the Functionality of Large- Scale Networks. Submitted.

[10] U. Münz, A. Papachristodoulou and F. Allgöwer. Multi-Agent System Consensus in Packet-Switched Networks. Submitted. Abridged version appears in the Proceedings of the European Control Conference, 2007.

[11] A. Papachristodoulou, A. Jadbabaie. Synchronization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics. In Proceedings of the IEEE Conference on Decision and Control, 2006.

[12] A. Papachristodoulou, A. Jadbabaie. Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays. In Proceedings of the IEEE Conference on Decision and Control, 2005.

[13] A. Papachristodoulou. Global stability analysis of a TCP/AQM protocol for arbitrary networks with delay. In Proceedings of the IEEE Conference on Decision and Control, 2004.

### Sum of Squares Techniques for Systems Analysis

[14] A. Papachristodoulou and S. Prajna. Analysis of non-polynomial systems using the sum of squares decomposition. In Positive Polynomials in Control, Springer-Verlag, 2004.

[15] A. Papachristodoulou, M. M. Peet and S. Lall. Constructing Lyapunov-Krasovskii Functionals for Nonlinear Delay-Differential Equations using Semidefinite Programming. Submitted.

[16] M. M. Peet, A. Papachristodoulou and S. Lall. Constructing Lyapunov Functionals for Linear Time Delay Systems. Submitted.

[17] A. A. Salinas-Varela, A. Papachristodoulou and J. Gonçalves. On L2 Error Bounds between Systems. In Proceedings of the International Symposium on Mathematical Theory of Networks and Systems, 2006.

[18] M. M. Peet, A. Papachristodoulou, and S. Lall. Positive Forms and Stability of Linear Time-Delay Systems. In Proceedings of the IEEE Conference on Decision and Control, 2006.

[19] A. Papachristodoulou. Robust stabilization of nonlinear time delay systems using convex optimization. In Proceedings of the IEEE Conference on Decision and Control, 2005.

[20] A. Papachristodoulou, S. Prajna and S. Glavaski. Sum of Squares in Industry: An Algorithmic Analysis Approach. Tutorial Session at the American Control Conference, 2005.

[21] A. Papachristodoulou, M. M. Peet and S. Lall. Constructing Lyapunov-Krasovskii Functionals for Linear Time Delay Systems. In Proceedings of the American Control Conference, 2005.

[22] A. Papachristodoulou. Analysis of nonlinear time delay systems using the sum of squares decomposition. In Proceedings of the American Control Conference, 2004.

[23] S. Prajna, A. Papachristodoulou, and F. Wu. Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach. In Proceedings of the Asian Control Conference, 2004.

[24] S. Prajna and A. Papachristodoulou. Analysis of switched and hybrid systems – beyond piecewise quadratic methods. In Proceedings of the American Control Conference, 2003.

[25] A. Papachristodoulou and S. Prajna. On the construction of Lyapunov functions using the sum of squares decomposition. In Proceedings of the IEEE Conference on Decision and Control, 2002.

[26] A. Papachristodoulou and M. M. Peet. On the Analysis of Systems Described by Classes of Partial Differential Equations. In Proceedings of the IEEE Conference on Decision and Control, 2006.

### Software

[27] S. Prajna, A. Papachristodoulou, and P. A. Parrilo. SOSTOOLS – Sum of Squares Optimization Toolbox, User’s Guide. Available at http://www.cds.caltech.edu/sostools, 2002.

[28] S. Prajna, A. Papachristodoulou, and P. A. Parrilo. Introducing SOSTOOLS: A general purpose sum of squares programming solver. In Proceedings of the IEEE Conference on Decision and Control, 2002.

[29] S. Prajna, A. Papachristodoulou, P. Seiler, and P. A. Parrilo. New developments in sum of squares optimization and SOSTOOLS. In Positive Polynomials in Control, Springer-Verlag, 2004.

### Applications

[30] S. Glavaski, D. Subramanian, K. Ariyur, R. Ghosh, N. Lamba and A. Papachristodoulou. A Nonlinear Hybrid Life Support System: Dynamic Modeling, Control Design, and Safety Verification. IEEE Transactions on Control Technology, in press.

[31] S. Glavaski, A. Papachristodoulou and K. Ariyur. Computational challenges of controlled hybrid system safety verification. In Hybrid Systems: Computation and Control, Springer-Verlag, 2005.

[32] K. Krishnaswamy, G. Papageorgiou, S. Glavaski, and A. Papachristodoulou. Analysis of aircraft pitch axis stability augmentation system using sum of squares optimization. In Proceedings of the American Control Conference, 2005.

[33] A. Papachristodoulou and C. Papageorgiou. Robust stability and performance analysis of a longitudinal aircraft model using sum of squares techniques. In Proceedings of the Mediterranean Control Conference, 2005.

[34] A. Papachristodoulou, J. C. Doyle, and S. H. Low. Analysis of nonlinear delay differential equation models of TCP/AQM protocols using sums of squares. In Proceedings of the IEEE Conference on Decision and Control, 2004.

[35] A. Papachristodoulou and F. E. C. Culick. Flight Mechanics of the Wright Aircraft 1903-1912. In AIAA 41st Aerospace Sciences Meeting and Exhibit, Paper number AIAA-2003-0097, 2003.