This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low computational complexity, the established controller design algorithms are applicable for large-scale systems. The theory and control strategies developed will not only be useful in handling large-scale positive delay systems with improved solvability and at lower cost, but also further our understanding of the system characteristics in other related areas, such as distributed coordination of networked multi-agent systems, formation control of multiple robots.
About the Author
2011.9–2015.8 The University of Hong Kong, Department of Mechanical Engineering, PhD
Supervisor: Prof. James Lam
2008.9–2011.4 Southeast University, Department of Mathematics, Master
Supervisor: Prof. Jinde Cao
2004.9–2008.7 Southeast University, Department of Mathematics, Bachelor
University Postgraduate Fellowship, 2011, HKU
Mechanical Engineering Outstanding Research Postgraduate Student, 2014, HKU
Outstanding Research Postgraduate Student, 2016, HKU
 Jun Shen, James Lam. Some extensions on the bounded real lemma for positive systems. IEEE Transactions on Automatic Control, 2015, DOI: 10.1109/TAC.2016.2606426.
 Jun Shen, James Lam. On the decay rate of discrete-time linear systems with cone invariance. IEEE Transactions on Automatic Control, 2015, DOI: 10.1109/TAC.2016.2610104.
 Jun Shen, James Lam. Input-output gain analysis for linear systems on cones. Automatica. Accepted for publication.
 Jun Shen, James Lam. Stability and performance analysis for positive fractional-order systems with time-varying delays. IEEE Transactions on Automatic Control, 2016, 61(9), 2676-2681.
 Jun Shen, James Lam. Static output-feedback stabilization with optimal L1-gain for positive linear systems. Automatica, 63: 248–253, 2016.
 Jun Shen, Wei Xing Zheng. Positivity and stability of coupled differential-difference equations with time-varying delays. Automatica, 57: 123–127, 2015.
 Jun Shen, Wei Xing Zheng. Stability analysis of linear delay systems with cone invariance. Automatica, 53: 30–36, 2015.
 Jun Shen, James Lam. Improved results on H∞ model reduction for continuous-time linear systems over finite frequency ranges. Automatica, 53: 79–84, 2015.
 Jun Shen, James Lam. On static output-feedback stabilization for multi-input multi-output positive systems. International Journal of Robust and Nonlinear Control, 25(16): 3154–3162, 2015.
 Jun Shen, James Lam. Containment control of multi-agent systems with unbounded communication delays. To appear in International Journal of Systems Science, 2014. DOI: 10.1080/00207721.2014.971092.
 Jun Shen, James Lam. ℓ∞/L∞-gain analysis for positive linear systems with unbounded time-varying delays. IEEE Transactions on Automatic Control, 60 (3), 857–862, 2015.
 Jun Shen, James Lam. Non-existence of finite-time stable equilibria in fractional-order nonlinear systems. Automatica, 50(2): 547–551, 2014.
 Jun Shen, James Lam. L∞-gain analysis for positive systems with distributed delays. Automatica, 50(1): 175–179, 2014.
 Jun Shen, James Lam. H∞ model reduction for discrete-time positive systems with inhomogeneous initial conditions. International Journal of Robust and Nonlinear Control, 25 (1): 88–102, 2015.
 Jun Shen, James Lam. On ℓ∞ and L∞ gains for positive systems with bounded time-varying delays. International Journal of Systems Science, 46(11): 1953–1960, 2015.
 Jun Shen, James Lam. H∞ model reduction for positive fractional order systems. Asian Journal of Control, 16(2): 441–450, 2014.
 Jun Shen, James Lam. State feedback H∞ control of commensurate fractional-order systems. International Journal of Systems Science, 45(3): 363–372, 2014.
[B1] Jianquan Lu, Jun Shen, Jinde Cao, and Jürgen Kurths. Consensus of networked multi-agent systems with delays and fractional-order dynamics, in “Consensus and Synchronization in Complex Networks”, 69–110, Berlin: Springer-Verlag, 2013.
Table of ContentsChapter 1. Introduction.- Chapter 2. Positive Systems with Retarded Delays.- Chapter 3. Positive Systems with Distributed Delays.- Chapter 4. Controller Synthesis of Positive Systems.- Chapter 5. Model Reduction for Discrete-time Positive Systems with Inhomogeneous Initial Conditions.- Chapter 6. Linear Delay Systems with Cone Invariance.- Chapter 7. Positivity and Stability of Coupled Diﬀerential-diﬀerence Equations with Time-varying Delays.- chapter 8. Conclusion and Future Work.