Integral Sliding Mode Anti-Disturbance Control for Markovian Jump Systems with Mismatched Disturbances

Abstract

This paper addresses an integral sliding mode-based anti-disturbance control algorithm for a type of Markovian jump systems (MJSs), which are influenced by different types of mismatched disturbances. On one hand, as for those disturbances that can be modeled, the disturbance observer (DO) method is introduced to realize the dynamical estimation of disturbances. Based on this, both the integral sliding surface (ISS) and the composite anti-disturbance controller are proposed in succession for rejecting unknown disturbances and guaranteeing the stability of the controlled MJS. Meanwhile, the states of the controlled system are ensured to reach ISS within a finite time. In addition, the L1 performance index is given to attenuate the effects of bounded disturbances. The controller and observer gains can be computed by using convex optimization techniques. The satisfactory stochastic stability and dynamical tracking performance are both also proved. Finally, the simulation results effectively verify all of the required performances.

Adaptive terminal sliding mode controller design for cyber‐physical systems under external disturbance and actuator cyber‐attack

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“…The attractive feature of integral‐type SMC is the omission of reaching phase required in conventional SMC techniques, and keeping of the system original order 47 . In the recent years, the progression has been made on integral‐type SMC approach for various complex dynamical systems consisting of singularly perturbed systems, descriptor systems, stochastic systems, Markov jump systems, and several types of hybrid systems 47–49 . However, this method has weaknesses in the face of severe external influences and uncertainties, which causes many problems such as high transient fluctuations and time delays.…”