Stability of Hybrid Dynamical Systems

Nonlinear systems theory is an active research area, where such questions as stability, robustness, and  optimal control are important issues interesting both from theoretical and practical viewpoints. In modern  applications, such systems appear in form of networks and interconnections.  Moreover, such effects as unknown disturbances, time-varying communication delays, an interaction of hardware and software layers may lead to a complex dynamics.  A distinctive feature of such processes is a combination of continuous and discontinuous behavior. There are several formal mathematical frameworks for modeling and analysis of this kind of systems. Traditionally, all these frameworks are called hybrid systems. An important property of hybrid systems is stability that is decisive for their performance and sustainability. In spite of a variety of developments, the methods for stability analysis are still not mature enough and cannot be applied to a range of real-world problems.

• to derive new sufficient conditions for asymptotic characterization of infinite dimensional impulsive differential equations
• to establish sufficient Lyapunov-like conditions for input-to-state stability of infinite dimensional systems for either unstable flows and stable jumps or stable flows and unstable jumps
• to develop new Lyapunov-like conditions for input-to-state stability of stochastic infinite dimensional systems
  
  

On robustness of impulsive stabilization.
Automatica, Elsevier BV,104, 48–56 (2019).
P. Feketa, N. Bajcinca.

Average Dwell-Time Conditions for Input-to-State Stability of Impulsive Systems.
Accepted at 21st IFAC World Congress (2020).
P. Bachmann, N. Bajcinca.

Average dwell-time for impulsive control systems possessing ISS Lyapunov function with nonlinear rates.
Proceedings  of  2019  18th  European  Control  Conference, Italy (2019).
P. Feketa, N. Bajcinca.

Stability of nonlinear impulsive differential equations with non-fixed moments of jumps.
In Proceedings of the 17th European Control Conference, Cyprus (2018).
P. Feketa, N. Bajcinca.

Hybrid systems
Input-to-state stability
Interconnected systems

Prof. Naim Bajcinca
Gottlieb-Daimler-Str. 42
67663, Kaiserslautern
Phone: +49 (0)631/205-3230
Fax: +49 (0)631/205-4201
naim.bajcinca@mv.uni-kl.de

State of Rhineland-Palatinate

Since 2017

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