Stabilisation of hybrid stochastic systems by disordered controllers

Abstract

This study considers the stabilisation problem of hybrid stochastic systems by regular and stochastic state feedback controllers whose operation modes suffer a disordering phenomenon. By introducing an augmented Markov chain, a new operation mode is used to describe such a disagreement. Without designing a controller with new operation mode directly, a kind of controllers only having original operation mode is developed by using the non-fragile control method, whose condition is given as linear matrix inequalities with equation constraints. Moreover, extensions to transition probability matrix with elementwise bounded uncertainties and being partially unknown are obtained. Simulation examples are used to demonstrate the effectiveness of the proposed methods.

Finite-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation

“…Thus, it is necessary and meaningful to consider this general case. Because of the obtained results with LMI forms here, it is concluded that they could be extended to the above general case, where some existing methods such as [5,10] will be used to deal with this uncertainty.…”

“…As we know, Markovian jump systems (MJSs) are very appropriate to describe dynamical systems experiencing changes in their structures or parameters randomly. Up to now, many important research topics of this kind of system, such as stability analysis [1][2][3][4], stabilization [5][6][7], ∞ control and filtering [8][9][10][11], output control [12,13], state estimation [14,15], adaptive control [16,17], and synchronization [18,19], have been considered. By investigating most results on the stability in the literature, it is seen that the classical Lyapunov stability guaranteeing the stability in an infinite-time interval was usually considered.…”

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

“…Moreover, some necessarily additional variables and inequalities are introduced to obtain LMI conditions, where the variables are to be computed instead of being given beforehand. Because of the given results with LMI forms, the above general case could be handled by exploiting the methods in this paper and [46,47] together.…”

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

“…Moreover, another case that operation mode is disordering or unmatched [48,49] is included, where S i F = S, but l satisfying λ l (k) = 1 is not equal to mode i satisfying r k = i. Finally, but not the last, when S i F ⊂ S, it is said that controller (3) with ∆ l ≡ I q is named to be a partially mode-available and unmatched controller.…”