Extended Dissipative Control for Markovian Jump Time-Delayed Systems with Bounded Disturbances

Abstract

<jats:p>In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.</jats:p>

H∞ controller design for singular Markov jump systems with time-delays

“…The research of Markov jump system originated in the 1960s. In recent years, with the rapid development of computer technology and the continuous improvement of mathematical theory, the analysis and design of Markov jump system have attracted extensive attention of scholars, 1–3 such as dissipative control problem, 4–6 adaptive control problem, 7,8 fault tolerant control problem, 9 fault detection problem, 10 and H ∞ filtering problem. 11,12…”

TS Fuzzy Robust Sampled-Data Control for Nonlinear Systems with Bounded Disturbances

“…The rationale of reachable set bounding is to identify an appropriate domain that can handle all reachable states of a dynamical system with respect to zero initial conditions with input disturbance conditions [20,21]. Moreover, systems have many real-life uses [22], such as gain minimization and control synthesis, and aircraft collision avoidance; therefore, it is significant to examine reachable dynamical systems, and several studies were published ( [23,24]).…”

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

“…On the other hand, the problem of passivity analysis has been studied by many researchers in many types of complex dynamic systems, including neural networks, networked models, and other biological models. The passivity property means that the increase of the energy stored inside the system is no more than that of the energy supplied to the system, which guarantees the stability of the concerned system [16]. Passivity theory, which was invented from electric circuit analysis, has been widely applied to many areas of dynamical systems such as complex systems, chaos control, signal processing, fuzzy control, and neural networks [17].…”