Submitted

@unpublished{WijnTren22pp,

title = {Impulse-controllability of system classes of switched differential algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/08/Preprint-WT220806.pdf, Preprint},

year  = {2022},

date = {2022-08-06},

urldate = {2022-08-06},

abstract = {In this paper impulse controllability of system classes containing switched DAEs is studied. We introduce several notions of impulse-controllability of system classes and provide a characterization of strong impulse-controllability of system classes generated by arbitrary switching signals. In the case of a system class generated by switching signals with a fixed mode sequence it is shown that either all or almost all systems are impulse-controllable, or that all or almost all systems are impulse-uncontrollable. Sufficient conditions for all systems to be impulse-controllable or impulse-uncontrollable are presented. Furthermore, it is observed that although all systems are impulse-controllable, the input achieving impulse-free solutions might still depend on the switching times in the future, which causes some causality issues. Therefore, the concept of (quasi-) causal impulse-controllability is introduced and system classes which are (quasi-) causal are characterized. Finally necessary and sufficient conditions for a system class to be causal given some dwell-time are stated.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{YinJaya22ppb,

title = {Stability of switched systems with multiple equilibria: a mixed stable-unstable subsystem case},

author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/08/Preprint-YJT220730.pdf, Preprint},

year  = {2022},

date = {2022-07-30},

urldate = {2022-07-30},

abstract = {This paper studies stability of switched systems that are composed of a mixture of stable and unstable modes with multiple equilibria. The main results of this paper include some sufficient conditions concerning set convergence of switched nonlinear systems. We show that under suitable dwell-time and leave-time switching laws, trajectories converge to an initial set and then stay in a convergent set. Based on these conditions, LMI conditions are derived that allow for numerical validation of practical stability of switched affine systems, which include those with all unstable modes. Two examples are provided to verify the theoretical results.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{LeeBerg22pp,

title = {Edge-wise funnel output synchronization of heterogeneous agents with relative degree one},

author = {Jin Gyu Lee and Thomas Berger and Stephan Trenn and Hyungbo Shim},

url = {https://stephantrenn.net/wp-content/uploads/2022/06/Preprint-LBTS220629.pdf, Preprint

https://arxiv.org/abs/2110.05330, ArXiV},

year  = {2022},

date = {2022-06-29},

urldate = {2021-10-11},

abstract = {When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior which is governed by a simple algebraic average of the node dynamics called the blended dynamics.

This finding has been utilized for designing heterogeneous multi-agent systems by building the desired blended dynamics first and then splitting it into the node dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know global information such as the number of participating nodes, the graph structure, and so on, which prevents a fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this issue, the idea of funnel control, which is a method for adaptive gain selection, can be exploited for a node-wise coupling, but the price to pay is that the collective emergent behavior is no longer governed by a simple average of the node dynamics. Our analysis reveals that this drawback can be avoided by an edge-wise design premise, which is the idea that we present in this paper. After all, we gain benefits such as a fully decentralized design without global information, collective emergent behavior being governed by the blended dynamics, and the plug-and-play operation based on edge-wise handshaking between two nodes.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{ChenTren22ppb,

title = {On impulse-free solutions and stability of switched nonlinear differential-algebraic equations},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/05/Preprint-CT220505.pdf, Preprint},

year  = {2022},

date = {2022-05-05},

urldate = {2022-05-05},

abstract = {In this paper, we study solutions and stability for switched nonlinear differential-algebraic equations (DAEs). A novel notion of solutions, called the impulse-free (jump-flow) solution, is proposed and a geometric characterization for its existence and uniqueness is given as a nonlinear version of the impulse-free condition used in, e.g., [22, 23], for linear DAEs. Then we show that the common Lyapunov functions stability conditions proposed in our previous work [12] (which differ from the ones in [23]) can be applied to switched nonlinear DAEs with high-index models which are not equivalent to the nonlinear Weierstrass form. Moreover, we generalize the commutativity stability conditions [27] for switched nonlinear ordinary differential equations to the nonlinear DAEs case. Finally, some simulation results of switching electrical circuits and numerical examples are given to illustrate the usefulness of the proposed stability conditions.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{HossTren22ppc,

title = {Midpoint based balanced truncation for switched linear systems with known switching signal},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/05/Preprint-HT220422.pdf, Preprint},

year  = {2022},

date = {2022-04-22},

abstract = {We propose a novel model reduction approach for switched linear systems with known switching signal. The class of considered systems encompasses switched systems with mode-dependent state-dimension as well as impulsive systems. Our method is based on a suitable definition of (time-varying) reachability and observability Gramians and we show that these Gramians satisfy precise interpretations in terms of input and output energy. Based on balancing the midpoint Gramians, we propose a piecewise-constant projection based model reduction resulting in a switched linear system of smaller size.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{HossTren22ppb,

title = {Reduced realization for switched linear systems with known mode sequence},

author = {Sumon Hossain and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/05/Preprint-HT220413.pdf, Preprint

https://doi.org/10.5281/zenodo.6410136, Matlab sources},

year  = {2022},

date = {2022-04-13},

urldate = {2022-04-13},

abstract = {We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input-output behavior. Our approach is based in considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition. A key feature of our approach is that only the mode sequence of the switching signal needs to be known and not the exact switching times. However, the size of a minimal realization will in general depend on the mode durations, hence it cannot be expected that our method always leads to minimal realization. Nevertheless, we show that our method is optimal in the sense that a repeated application doesn’t lead to a further reduction and we also highlight a practically relevant special case, where minimality is achieved.},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{YinJaya22ppa,

title = {On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time},

author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/04/Preprint-YJT220315.pdf, Preprint},

year  = {2022},

date = {2022-03-15},

urldate = {2022-03-15},

note = {submitted},

keywords = {},

pubstate = {published},

tppubtype = {unpublished}

}