Distributed output feedback control of decomposable LPV systems with delay and switching topology: application to consensus problem in multi-agent systems

Abstract

This paper presents distributed output feedback control of a class of distributed linear parameter varying systems with switching topology and parameter varying time delay. To formulate the synthesis conditions for the distributed controller in terms of LMIs, the delay dependent bounded-real lemma based on parameter-dependent Lyapunov-Krasovskii functionals is used. The efficacy of the result is illustrated by applying it to two real-world examples pertaining to the consensus problem of multi-agent systems.

Dynamic output feedback control of delayed linear parameter varying systems with piecewise constant parameters: A clock‐dependent L–K approach

“…Since we are interested in induced ‐gain performance for the closed‐loop system. Therefore, we define the worst‐case ‐gain 25 for system from the exogenous input w to the desired controlled output z (with u ≡ 0) as where | · | 2 denotes the Euclidean norm.…”

“…In this article, we consider a class of LPV systems with piecewise constant parameters 16 that can be considered a generalization of switched linear systems where the subsystems take values within some interval instead of some finite set. This class of LPV systems can model large‐scale interconnected systems, networked control systems, and multiagent systems where switching topology is an inevitable phenomenon because the interconnection links may change over time due to various reasons 17 . For example, communicating mobile agents may lose an existing connection due to the presence of an obstacle.…”

“…For example, communicating mobile agents may lose an existing connection due to the presence of an obstacle. On the other hand, a new connection may be established between the agents when they come close to each other in an effective range of detection 17 . LPV systems with piecewise constant parameters also arise naturally in synchronous buck converters with piecewise constant loads 18 and as a simplifying assumption in the control of LPV sampled‐data systems 19 .…”

“…Time delays frequently appear in communication networks, milling machines, aircraft, robotized teleoperation, and many other domains; see, for example, References 22,24. Time delays can also adversely affect the stability of the LPV systems 8,25‐32 . This fact motivated us to consider delayed LPV systems with piecewise constant parameters.…”

Distributed Output Feedback Control of Decomposable LPV Systems with Delay: Application to Multi-agent Nonholonomic Systems

“…++ are constant matrices, A a , b ,B,Ĉ a ,Ĉ b and R are ρ-dependent matrices, and γ > 0 is a scalar. Moreover, if LMIs have feasible solutions, the controller matrices appearing in (7) and (8) are given bȳ The proof of Theorem 2 follows directly from our journal version [31].…”