Design proportional‐integral‐derivative/proportional‐derivative controls for second‐order time‐varying switched nonlinear systems

Abstract

Summary Based on proportional‐integral‐derivative (PID)/PD controls, we in the article investigate the tracking problem of a class of second‐order time‐varying switched nonlinear systems. To start with, for tracking a given point under arbitrary switching signals, we propose a sufficient condition about PID controller parameters, which can be implicitly described as semialgebraic sets. Successively, we consider the tracking problem under average dwell time (ADT)‐based switching signals and propose an alternative sufficient condition about PID controller parameters. Especially, for tracking an equilibrium point of the system without controls, we can further simply utilize the proportional‐derivative control and similarly construct corresponding semialgebraic conditions about proportional‐derivative controller parameters under arbitrary switching signals and ADT‐based switching signals. Finally, two examples are given to show the applicability of our theoretical results.

Uniform exponential stability criteria with verification for nonautonomous switched nonlinear systems with uncertainty

“…In our future works, we would like to construct a proper uncertainty‐independent Lyapunov function to gain a necessary and sufficient condition for the GES of UNSNS. Besides, extending our proposed results to discrete‐time UNSNS 40,48 and the multiagent systems with switching topology, 7‐11 and even designing the proportional‐integral‐derivative controller for UNSNS based on dwell time and scalar functions 49,50 are interesting. Moreover, the computation issue of more general UNSNS is also worthy to be investigated.…”

Leader‐following consensus of stochastic dynamical multi‐agent systems with fixed and switching topologies under proportional‐integral protocols

“…By adopting distributed PI protocols, consensus of directed heterogeneous linear MASs were investigated and sufficient conditions for selecting the feedback gains were obtained in [34]. In [35], She et al studied the consensus tracking problem in second-order nonlinear time-varying systems underlying switching topologies by means of PID protocols. Gu et al considered the PI protocols design problem for leaderless consensus of nonlinear networked systems with stochastic dynamics, and put forward several sufficient conditions for choosing feedback gains [36].…”

“…Compared with the consensus protocols for second-order nonlinear MASs with switching topologies in [37], the proposed protocols utilize not only the current information but also the previous information of the states for the considered systems, which can improve the consensus performance of the dynamical MASs. Although some consensus results have been derived in [33][34][35] for MASs underlying PI protocols, the problem is solved in this article for MASs with stochastic dynamics and switching topologies simultaneously. Furthermore, in contrast to the recent work [36], the leader-follower consensus problems with fixed and switching topologies are addressed in this article, which pose more challenge on the PI protocols design.…”