arXiv subjects

Atreyee Kundu

Publications and source records attributed to Atreyee Kundu.

29 records · Page 2Linked to original sources

arXiv2019

A new condition for stability of switched linear systems under restricted minimum dwell time switching

We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched system is stable under all switching signals that obey the given restriction. The primary tool for our analysis is commutation relations between the subsystem matrices. Our stability conditions are robust with respect to small perturbations in the elements of these matrices. In case of arbitrary switching (i.e., given minimum dwell time = 1), we recover the prior result [1,Proposition 1] as a special case of our result.

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arXiv2019

On the design of stabilizing cycles for switched linear systems

Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known technique in the literature. This paper deals with a new {method to design} these cycles for stability of switched linear systems. We employ properties of the subsystem matrices and mild assumption on the admissible switches between the subsystems {for this purpose}. In contrast to prior works, {our construction of} stabilizing cycles does not involve design of Lyapunov-like functions and storage of sets of scalars in memory prior to the application of a cycle detection algorithm. As a result, {the} techniques {proposed in this paper} offer improved numerical tractability.

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arXiv2019

Robust matrix commutator conditions for stability of switched linear systems under restricted switching

This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under which they admit a set of switching signals that obeys the given restrictions on dwell times and preserves stability of the resulting switched system. Our analysis relies on combinatorial arguments applied to matrix commutators and avoids the employment of Lyapunov-like functions. The proposed set of stabilizing switching signals is characterized in terms of duration of activation of Schur stable subsystems and non-consecutive activation of distinct unstable subsystems.

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arXiv2019

Stabilizing Scheduling Policies for Networked Control Systems

This paper deals with the problem of allocating communication resources for Networked Control Systems (NCSs). We consider an NCS consisting of a set of discrete-time LTI plants whose stabilizing feedback loops are closed through a shared communication channel. Due to a limited communication capacity of the channel, not all plants can exchange information with their controllers at any instant of time. We propose a method to find periodic scheduling policies under which global asymptotic stability of each plant in the NCS is preserved. The individual plants are represented as switched systems, and the NCS is expressed as a weighted directed graph. We construct stabilizing scheduling policies by employing cycles on the underlying weighted directed graph of the NCS that satisfy appropriate contractivity conditions. We also discuss algorithmic design of these cycles.

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arXiv2018

On asymptotic characterization of destabilizing switching signals for switched linear systems

This paper deals with classes of (de)stabilizing switching signals for switched systems. Most of the available conditions for stability of switched systems are sufficient in nature, and consequently, their violation does not conclude instability of a switched system. The study of instability is, however, important for obvious reasons. Our contributions are twofold: Firstly, we propose a class of switching signals under which a continuous-time switched linear system is unstable. Our characterization of instability depends solely on the asymptotic behaviour of frequency of switching, frequency of transition between subsystems, and fraction of activation of subsystems. Secondly, we show that our class of destabilizing switching signals is a strict subset of the class of switching signals that does not satisfy asymptotic characterization of stability recently proposed in the literature. This observation identifies a gap between asymptotic characterizations of stabilizing and destabilizing switching signals for switched linear systems. The main apparatus for our analysis is multiple Lyapunov-like functions.

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arXiv2017

Stabilizing switching signals: a transition from point-wise to asymptotic conditions

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an umbrella framework. We achieve this in two steps: Firstly, given a family of systems, possibly containing unstable dynamics, we propose a new and general class of stabilizing switching signals. Secondly, we demonstrate that prior results based on both point-wise and asymptotic characterizations follow our result. This is the first attempt in the switched systems literature where these switching signals are unified under one banner.

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arXiv2016

Observability and controllability analysis of linear systems subject to data losses

We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject to disruptions (data losses) in the feedback loop, where the set of possible data loss sequences is captured by an automaton. As such, the results are applicable in the context of shared (wireless) communication networks and/or embedded architectures where some information on the data loss behaviour is available a priori. We propose an algorithm for deciding observability (or the absence of it) for such systems, and show how this algorithm can be used also to decide other properties including constructibility, controllability, reachability, null-controllability, detectability and stabilizability by means of relations that we establish among these properties. The main apparatus for our analysis is the celebrated Skolem Theorem from linear algebra. Moreover, we study the relation between the model adopted in this paper and a previously introduced model where, instead of allowing dropouts in the feedback loop, one allows for time varying delays.

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arXiv2015

A graph theoretic approach to input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS. We allow non-ISS systems in the family and our analysis involves graph-theoretic arguments. A weighted digraph is associated to the switched system, and a switching signal is expressed as an infinite walk on this digraph, both in a natural way. Our class of stabilizing switching signals (infinite walks) is periodic in nature and affords simple algorithmic construction.

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arXiv2015

Generalized switching signals for input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of continuous-time switched nonlinear systems. Given a family of systems with exogenous inputs such that not all systems in the family are ISS, we characterize a new and general class of switching signals under which the resulting switched system is ISS. Our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval, unlike in the case of average dwell time switching. We also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results.

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arXiv2014

Deterministic and probabilistic algorithms for stabilizing discrete-time switched linear systems

In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the switching signal is expressed as an infinite walk on this weighted digraph. We employ graph-theoretic tools and discuss different algorithms for designing walks whose corresponding switching signals satisfy the stabilizing switching conditions proposed in [12]. We also address the issue of how likely/generic it is for a family of systems to admit stabilizing switching signals, and under mild assumptions give sufficient conditions for the same. Our solutions have both deterministic and probabilistic flavours.

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arXiv2013

Stabilizing switching signals for switched linear systems

This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which the switched linear system generated by it and the family of systems is globally asymptotically stable. Our characterization of such stabilizing switching signals involves the asymptotic frequency of switching, the asymptotic fraction of activation of the constituent systems, and the asymptotic densities of admissible transitions among them. Our techniques employ multiple Lyapunov-like functions, and extend preceding results both in scope and applicability.

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