Stability of Switched Linear Differential Systems

Abstract

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions.

Dissipative Switched Linear Differential Systems

“…In such approaches, the dynamical modes share a global state space. In [23], [24], we argued that in many real-life situations the dynamical modes of switched systems do not share the same state space. Examples include multi-controller control systems, power converters, power sources with multiple loads, charging stations for electric vehicles, hybrid renewable energy systems, etc.…”

“…Examples include multi-controller control systems, power converters, power sources with multiple loads, charging stations for electric vehicles, hybrid renewable energy systems, etc. Moreover, since switched systems can be studied in higher-order terms (see [22], [23], [24], [30], [32], [38]), the use of state space representations themselves is not a fundamental requirement.…”

“…In [24], we introduced a framework for the study of switched linear differential systems (SLDS), where each dynamical mode is associated with a mode behaviour, i.e. the set of trajectories satisfying higherorder linear differential equations.…”

A systematic approach to constant power load stabilization by passive damping

“…In this paper we present a design methodology for such passive-damping filters, based on a novel approach to model linear differential switched systems, that also provides accurate piecewise linear approximations of the behavior of many power systems (see [8], [10], [11], [12]). This framework offers several advantages over the classical one based on state space descriptions sharing the same state space (see [9], [11]).…”

“…This framework offers several advantages over the classical one based on state space descriptions sharing the same state space (see [9], [11]). Moreover, in our framework it is straightforward to accommodate more general descriptions of the instabilitygenerating mechanism than the traditional negative resistance one (see [1]), e.g.…”