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Stability analysis of switched linear systems

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Switched linear systems are an important subclass of hybrid systems and consist of a finite number of linear time-invariant systems with continuous dynamics and some switching mechanism that orchestrates between them. Dynamical systems of this class can be found in various fields of engineering applications, such as aviation technology, power electronics, automotive engineering or power generation.

One of the most important system properties is of course stability. We have studied analytical tools for investigating stability of switched linear systems [1] [2] [3], but have also explored issues in control design. In particular, in [4] [5] [6] [7] , the concept of common left eigenstructure assignment is used to achieve exponential stabilisation of switched linear systems with single and multiple inputs.

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  1. Ishan Pendharkar, Kai Wulff, Jörg Raisch. On the construction of quadratically stable switched linear systems with multiple component systems. In Proceedings of the Conference on Decision and Control, 2007, pages 6274 - 6279,
  2. Ishan Pendharkar, Kai Wulff, Jörg Raisch. A behavioral-theoretic approach to quadratic stability of switched linear systems. In 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, 2007.
  3. I. Pendharkar, K. Wulff, J. Raisch. On stability of switched differential algebraic systems – conditions and applications. In Proc. IFAC World Congress, Seoul, 2008.
  4. Kouhi, Y., Bajcinca, N.. On the left eigenstructure assignment and state feedback design. In Proc. of the American Control Conference, pages 4326-4327, 2011.
  5. Kouhi, Y., Bajcinca, N.. Robust control of switched linear systems. In Proc. Conf. on Decision and Control and European Control Conference, 2011.
  6. Kouhi, Y., Bajcinca, N.. Nonsmooth control design for stabilizing switched linear systems by left eigenstructure assignment. In Proc. IFAC World Congress, pages 380-385, 2011.
  7. Kouhi, Y., Bajcinca, N.,, Raisch, J.,, Shorten, R.. A new stability result for switched linear systems. In Proc. of the European Control Conference, pages 2152-2156, 2013.

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