Observer-Based $$H_\infty $$ H ∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

Abstract

The paper is concerned with the observer-based H ∞ sliding mode controller design for a class of uncertain stochastic singular time-delay systems subjected to input nonlinearity. Using the sliding mode control, a robust law is established to guarantee the reachability of the sliding surface in a finite time interval, and the sufficient condition for asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level is presented in terms of linear matrix inequalities. Finally, an example illustrates the proposed method.

Observer‐based adaptive control of uncertain stochastic singular systems via integral sliding mode technique

“…, (20) is held since the SMDs is in the sliding mode initially, and after some finite‐time , the system will be kept in the sliding mode again. However, it is noted that the counterpart of [33] may not be ensured, because its SMDs may not operate from the initial time due to the fact that the system may be not on the sliding surface initially, i.e. the SMDs will work after some finite‐time , and and may not always equal to zeros, which results in (20) may not be ensured in this way.…”

“…Up to now, by combining the advantages of both the SMC and observer effectively, sliding mode observer strategy [31, 32] has been verified to be implementable and successfully applied to many practical systems. In [33], observer‐based SMC design for uncertain stochastic singular time‐delay systems subjected to input non‐linearity has been considered, whereas the inherent attribute of this kind of systems, i.e. the existence of its solution, the regularity and freeness of impulse, has not been discussed.…”

An efficient observer design method for singular discrete-time systems with time-delay and nonlinearity: LMI approach

“…Osorio-Gordillo et al [25] are concerned with the fault-detection and isolation for singular systems via a dynamical observer. In [26], the design method of an observer-based H 1 SMC for the uncertain time delay stochastic singular systems with input nonlinearity was planned. In [27], the design approach to the full-order observer was concerned with time delay singular systems with Lipschitz nonlinearities.…”

“…combining Eqs (26). and(29) and using Lemma 2, inequality V (k) < 0 is satis ed if there exists a non-negative scalar such that:2 T A LC) T P (T A LC) P + Q +2 1…”

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

“…Markovian jumping cases (25,26) . Up to date and to the best of our knowledge, the observer-based control problem for a discrete-time Markovian jumping singular system (DMJSS) does not have clear investigation and still remains challenges.…”