LMI-based Controller Design for Leaky-integrator MIMO Systems
Keywords:
LMIs, delta ISS, MIMO systems, Leaky-integratorAbstract
Leaky-integrator systems have attracted attention due to their capability of capturing the gradual loss of the system states. Thanks to the advantages of taking into consideration the leaky effect on gradual loss of systems states, leaky-integrator systems have been applied in biological modeling and electronic circuit design. However, robust control design conditions for such systems are insufficiently developed. In the existing literature, global asymptotic stability analysis has been conducted on leaky-integrator systems, however, such analysis neglects the effects of the inputs and is based solely on single-input single-output systems. The stability analysis for leaky-integrator multi-input multi-output (MIMO) systems is yet to be developed. This paper proposes a controller design method based on Linear Matrix Inequality (LMI) for a class of leaky-integrator MIMO systems. Compared to the existing literature, controllers that guarantee incremental input-to-state stability for leaky-integrator systems are established. In this paper, a set of linear matrix inequalities regarding the controller design conditions is derived based on the incremental input-to-state stability. An observer structure for the considered leaky-integrator MIMO systems is also presented, along with the observer design conditions. A numerical simulation example showcases the effectiveness of the proposed approach. The simulation results demonstrate that the developed LMI conditions are applicable for a class of leaky-integrator MIMO systems. With the proposed controller and observer design conditions, the leaky-integrator MIMO system can be stabilized and achieve the control goal of trajectory tracking.References
[1] H. Jaeger, The ’echo state’ approach to analysing and training recurrent neural networks, GMD-Report 148, German National Research Institute for Computer Science, 2001.
[2] S. Zhou, Z. O’Neill, and C. O’Neill, A review of leakage detection methods for district heating networks, Applied Thermal Engineering, 137, 2018, 567–574.
[3] C. Teeter, R. Iyer, V. Menon, N. W. Gouwens, D. Feng, J. Berg, A. Szafer, N. Cain, H. Zeng, M. Hawrylycz, C. Koch, and S. Mihalas, Generalized leaky integrate-and-fire models classify multiple neuron types, Nature Communications, 9, 2018, 709.
[4] S. S. D. P. Ayyagari, R. D. Jones, and S. J. Weddell, Optimized echo state networks with leaky integrator neurons for EEG-based microsleep detection, International Conference of the IEEE Engineering in Medicine and Biology Society, 2015, 3775–3778.
[5] V. Kornijcuk, H. Lim, I. Kim, J.-K. Park, W.-S. Lee, J.-H. Choi, B. J. Choi, and D. S. Jeong, Scalable excitatory synaptic circuit design using floating gate based leaky integrators, Scientific Reports, 7, 2017, 17579.
[6] X. Chen, Adaptive sliding mode control for discrete-time multi-input multi-output systems, Automatica, 42, 2006, 427–435.
[7] D. Xu, Y. Shi, I. W. Tsang, Y.-S. Ong, C. Gong, and X. Shen, Survey on multi-output learning, IEEE Transactions on Neural Networks and Learning Systems, 31, 2020, 2409–2429.
[8] F. Bonassi and R. Scattolini, Recurrent neural network-based internal model control design for stable nonlinear systems, European Journal of Control, 65, 2022, 100632.
[9] B. Yildiz, H. Jaeger, and S. J. Kiebel, Re-visiting the echo state property, Neural Networks, 35, 2012, 1–9.
[10] W. D’Amico, A. L. Bella, and M. Farina, An incremental input-to-state stability condition for a class of recurrent neural networks, IEEE Transactions on Automatic Control, 69, 2024, 2221–2236.
[11] D. Angeli, A Lyapunov approach to incremental stability properties, IEEE Transactions on Automatic Control, 47, 2002, 410–421.
[12] H. Deng, C. Stoica, and M. Chadli, Leaky-integrator echo state network incremental ISS stability analysis, IEEE Control Systems Letters, 9, 2025, 1814–1819.
[13] S. Dutta, V. Kumar, A. Shukla, and N. Bhat, Leaky integrate and fire neuron by charge discharge dynamics in floating-body MOSFET, Scientific Reports, 7, 2017, 257.
[14] J. P. Jordanou, E. A. Antonelo, and E. Camponogara, Online learning control with echo state networks of an oil production platform, Engineering Applications of Artificial Intelligence, 85, 2019, 214–228.
[15] F. Bayer, M. Bürger, and F. Allgöwer, Discrete-time incremental ISS: A framework for robust NMPC, European Control Conference, 2013, 2068–2073.
[16] D. N. Tran, B. S. Rüffer, and C. M. Kellett, Incremental stability properties for discrete time systems, IEEE Conference on Decision and Control, 2016, 477–482.
[17] J. Doyle, B. Francis, and A. Tannenbaum, Feedback Control Theory, Dover Books on Electrical Engineering Series, Dover, 2009.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Hao Deng, Cristina Stoica, Mohammed Chadli, Daniel Ossmann
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:Authors hold and retain copyright, and grant the journal right of first publication, with the work after publication simultaneously licensed under a Creative Commons Attribution 4.0 License CC BY that permits any use, reproduction and distribution of the work and article without further permission provided that the original work is properly cited.
Authors are permitted and encouraged to post their work online in institutional repositories, website and other social media before and after publication, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
