Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

Abstract

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

Stabilization of Discrete-Time Markovian Jump Systems by a Partially Mode-Unmatched Fault-Tolerant Controller

“…Based on representation (7), it is obvious that condition (17) is equivalent to (6). This completes the proof.…”

“…On the other hand, some references [5,6,17,26] have considered other general cases that the transition rate matrix referred to continuous-time case is partially unknown, uncertain or depends on the random sojourn time. Even in reference [20], the partially accessible mode information is also referred to transition rate matrix partially unknown.…”

“…It also has been widely studied in the field of industrial process control, space flight, medical treatment, electric power and economy. During the past few decades, many important results based on kinds of systems have emerged, such as stability analysis [1][2][3][4][5][6], stabilization [7][8][9][10], delay case [11][12][13], output control [14,15], H ∞ control [16][17][18][19] and filtering [20][21][22], robust control [23][24][25], sliding control [26], state estimation [27], fault detection [28], synchronization [29,30], and so on.…”

Improved Reduced-Order Fault Detection Filter Design for Polytopic Uncertain Discrete-Time Markovian Jump Systems with Time-Varying Delays

“…When the components or instrument fault had been found, through the fault-tolerant control approach, 2 Complexity the stable system performance has always be maintained. Therefore, many fault detection methodologies have been addressed in engineering applications, since failure may result in disastrous consequences and hazards for personnel, plant, and environment (see, e.g., [19][20][21][22]). For instance, many fruitful results to detect fault of systems without timevarying delays have been reported.…”

Adaptive Sliding Mode Control for High-Frequency Sampled-Data Systems with Actuator Faults

“…A great deal of attention has been paid to networked control systems (NCSs) in recent years [13][14][15][16][17], because they are able to be combined with different kinds of practical systems widely [18][19][20]. It should be noticed that, in modern industrial systems, the high frequency sampling situation always exists.…”