On Output Feedback Stabilization of Time-Varying Decomposable Systems with Switching Topology and Delay

This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems with switching topology as equivalent LPV systems with a piecewise constant parameter. In the second step, we design stabilizing output feedbacks for these LPV systems in the presence of a time-varying output delay using a trajectory-based stability analysis approach. We do not impose any constraint on the delay derivative. Finally, we illustrate our approach by applying it to the consensus problem of non-holonomic agents.

[1]  M. Mesbahi,et al.  Formation flying control of multiple spacecraft via graphs, matrix inequalities, and switching , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[2]  Mihailo R. Jovanovic,et al.  On the ill-posedness of certain vehicular platoon control problems , 2005, IEEE Transactions on Automatic Control.

[3]  Bahram Shafai,et al.  Decomposition-Based Distributed Control for Continuous-Time Multi-Agent Systems , 2013, IEEE Transactions on Automatic Control.

[4]  P.G. Voulgaris,et al.  Distributed control of large segmented telescopes , 2006, 2006 American Control Conference.

[5]  Saeed Ahmed,et al.  Distributed Output Feedback Control of Decomposable LPV Systems with Delay: Application to Multi-agent Nonholonomic Systems , 2019, 2019 18th European Control Conference (ECC).

[6]  Bin Zhou,et al.  Consensus of high-order multi-agent systems with large input and communication delays , 2014, at - Automatisierungstechnik.

[7]  Long Wang,et al.  Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays , 2009, IEEE Transactions on Automatic Control.

[8]  Rifat Sipahi,et al.  Consensus Control Under Communication Delay in a Three-Robot System: Design and Experiments , 2016, IEEE Transactions on Control Systems Technology.

[9]  Corentin Briat,et al.  Linear Parameter-Varying and Time-Delay Systems , 2015 .

[10]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[11]  Bahram Shafai,et al.  Robust distributed control of decomposable systems with switching network topology , 2010, 49th IEEE Conference on Decision and Control (CDC).

[12]  A. Jadbabaie,et al.  Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization , 2010, IEEE Transactions on Automatic Control.

[13]  Muhammad Zakwan.  Dynamic $L_{\text{2}}$ Output Feedback Stabilization of LPV Systems With Piecewise Constant Parameters Subject to Spontaneous Poissonian Jumps , 2020, IEEE Control Systems Letters.

[14]  Francesco Borrelli,et al.  Distributed LQR Design for Identical Dynamically Decoupled Systems , 2008, IEEE Transactions on Automatic Control.

[15]  Michel Verhaegen,et al.  Distributed Control for Identical Dynamically Coupled Systems: A Decomposition Approach , 2009, IEEE Transactions on Automatic Control.

[16]  Corentin Briat.  Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & Control , 2014 .

[17]  Fatihcan M Atay,et al.  The consensus problem in networks with transmission delays , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  Corentin Briat,et al.  Stability analysis and control of a class of LPV systems with piecewise constant parameters , 2015, Syst. Control. Lett..

[19]  Christian Hoffmann,et al.  Robust control of decomposable LPV systems , 2014, Autom..

[20]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[21]  Milad Siami,et al.  Interplay between performance and communication delay in noisy linear consensus networks , 2016, 2016 European Control Conference (ECC).

[22]  Herbert Werner,et al.  LPV Formation Control of Non-Holonomic Multi-Agent Systems , 2014 .

[23]  Karl Henrik Johansson,et al.  Consensus under communication delays , 2008, 2008 47th IEEE Conference on Decision and Control.

[24]  Dimitry M. Gorinevsky,et al.  Feedback controller design for a spatially distributed system: the paper machine problem , 2003, IEEE Trans. Control. Syst. Technol..

[25]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[26]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[27]  Saeed Ahmed,et al.  Distributed output feedback control of decomposable LPV systems with delay and switching topology: application to consensus problem in multi-agent systems , 2020, Int. J. Control.

[28]  Frédéric Mazenc,et al.  Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach , 2018, Autom..

[29]  A. Betser,et al.  Flying in formation using a pursuit guidance algorithm , 2005, Proceedings of the 2005, American Control Conference, 2005..

[30]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[31]  Zhisheng Duan,et al.  Cooperative Control of Multi-Agent Systems: A Consensus Region Approach , 2014 .