Atreyee Kundu

Stabilizing Switching Signals for Switched Systems

This article deals with stability of continuous-time switched systems under constrained switching. Given a family of systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which the switched 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.

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.

Stabilizing discrete-time switched linear systems

This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that stabilize a switched system generated by the switching signal and the given family of systems. Secondly, given a switched system, a sufficient condition for the existence of the proposed switching signal is derived by expressing the switching signal as an infinite walk on a directed graph representing the switched system. Thirdly, given a family of linear systems, we propose an algorithmic technique to design a switching signal for stabilizing the corresponding switched system.

On Lyapunov-Metzler Inequalities and S-Procedure Characterizations for the Stabilization of Switched Linear Systems

In this note we present connections between two celebrated tools for the design of stabilising switching laws for continuous-time and discrete-time switched linear systems, namely Lyapunov-Metzler inequalities and S-procedure.

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.

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

Abstract 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.

Stabilizing discrete-time switched systems with inputs

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of systems with exogenous inputs, we present a discrete-time analog of the class of stabilizing switching signals proposed in [6]. We allow non-ISS systems in the family and our analysis relies on multiple ISS-Lyapunov-like functions. We identify a subclass of average dwell time switching signals in our setting, and establish a discrete-time counterpart of an ISS version of [10, Theorem 2] as a corollary of our main result.

Stabilizing switched nonlinear systems under restricted switching

This paper deals with input/output-to-state stability (IOSS) of continuous-time switched nonlinear systems under restricted switching. The switching signals obey restrictions on: (i) transitions between subsystems, and (ii) dwell time on subsystems. Given a family of systems, possibly containing non-IOSS dynamics, we present an algorithm to construct a time-dependent switching signal that guarantees IOSS of the resulting switched system under these restrictions. The main apparatus for our analysis are multiple Lyapunov-like functions and graph-theoretic tools.

Randomized algorithms for stabilizing switching signals

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.

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 behavior 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 Skolems 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.