H_∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

Abstract

The problem of H ∞ robust control based on event-triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event-triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H ∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean-square admissible and has a prescribed H ∞ performance . Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method. KEYWORDS descriptor systems, event-triggered, linear matrix inequalities (LMIs), Markovian jump, stochastic control 790

$H_{\infty}$ Controller Design for Singular Stochastic Markovian Jump System With Time-Varying Delay

“…Remark2: Recently, many research has been given dissipative control and H ∞ filtring for the singular Markovian systems [11], [13], [19], [24], [26].However, in practise, the stochastic phenomenon are inevitable.In this paper, the author given the detailed Itô formula with singular and Markov jumping.…”

Discrete‐time dynamic event‐triggered H∞ control of uncertain neural networks subject to time delays and disturbances

“…In comparison with existing methods in the literature, [9][10][11][12][13][14][32][33][34][35][36] the main advantages of the method in this article are:…”

“…Event‐triggered $$$ {H}_{\infty } $$$ control design problem for dynamical systems was discussed in References 32‐36. In particular, the $$$ {H}_{\infty } $$$ containment control of multiagent systems under event‐triggered communication scheduling was considered in Reference 32.…”

“…In particular, the $$$ {H}_{\infty } $$$ containment control of multiagent systems under event‐triggered communication scheduling was considered in Reference 32. In Reference 33, the authors investigated the problem of event triggered finite time $$$ {H}_{\infty } $$$ boundedness of uncertain Markov jump neural networks with distributed time varying delays while some new approaches to event‐triggered $$$ {H}_{\infty } $$$ control were proposed in References 34‐36.…”

“…In comparison with existing methods in the literature, 9‐14,32‐36 the main advantages of the method in this article are: In contrast to $$$ {H}_{\infty } $$$ control design methods, 9‐14 where the controller $$$ u(t)= Kx(t) $$$ is continuous, the event‐triggered controller $$$ u(t)= Kx\left({t}_k\right) $$$ in this article is only updated at $$$ {\left\{{t}_k\right\}}_{k\in \mathbb{N}} $$$ which can save communication resources. Different from the methods in References 32‐36, which are based on continuous‐time ETMs, the one in this article is based on a Zeno‐free discrete‐time dynamic ETM which may reduce the utilization of communication resources while keeping the desired control performance. Moreover, since the Zeno‐free discrete‐time dynamic ETM depends on an internal dynamic variable, it can enlarge the time intervals between two consecutive triggering events. …”