Robust dynamic output feedback stabilization for uncertain singular Markovian jump systems with time‐varying delays

Abstract

The article investigates robust dynamic output feedback (DOF) stabilization for uncertain time-varying delays singular Markovian jump systems (SMJSs). First, by using improved Lyapunov-Krasovskii functional, sufficient conditions of robust admissibility (namely regularity, non-impulsiveness, and asymptotic stability) for unforced nominal time-varying delays SMJSs are given. Second, by constructing a DOF controller such that the resulting closed-loop system satisfies robust admissibility, the robust DOF stabilization problem is solved in terms of linear matrix inequalities via orthogonal complement technique. Finally, the availability and practicality of the prime results are certified by two numerical examples and a practical example of the oil catalytic cracking process.

Robust H∞$$ {H}_{\infty } $$ continuous‐discrete hybrid impulsive dynamic output feedback control for delays descriptor Markovian jump systems with multidimensional impulsive operator

“…48,49 The novel hybrid impulsive DOF controller combines the advantages of impulsive control and DOF control, has wonderful practicability in the control process and less dependent state information. 37,41 For each 𝜐 t = i ∈ , connecting (1) with (2), we obtain the following closed-loop time delays descriptor Markovian jump systems:…”

“…However, the continuous control can not be endured in many actual dynamic systems, in this case, a discrete impulsive DOF controller is needed to be proposed when $$$ t={t}_k $$$ 48,49 . The novel hybrid impulsive DOF controller combines the advantages of impulsive control and DOF control, has wonderful practicability in the control process and less dependent state information 37,41 …”

“…Definition (References 35 and 37) The unforced TDDMJS (3) is regular and impulse‐free, if for , the pencil $$$ \left(\tilde{E},{\overset{\widetilde }{A}}_{0i}\right) $$$ realizes regularity and nonimpulsiveness. The unforced TDDMJS (3) is stochastically stable, if there exists a scalar such that The unforced TDDMJS (3) is stochastically admissible, if the regularity, non‐impulsiveness and stochastic stability are achieved. The unforced TDDMJS system (3) achieves $$$ {H}_{\infty } $$$ performance level $$$ \gamma $$$, if for zero initial condition, the controlled output $$$ \mathfrak{Z}(t) $$$ satisfies …”

“…In recent years, the DOF control has been favored by many experts and scholars for its better flexibility and practicability in engineering control 34 . Reference 35 proposed the necessary and sufficient conditions for the DOF stabilization of continuous‐time DMJSs 36 ; studied a DOF $$$ {H}_{\infty } $$$ control for continuous‐time DMJSs 37 ; researched the issue of DOF $$$ {H}_{\infty } $$$ control for the uncertain DMJSs.…”

Output reachable set synthesis for singular Markovian jump systems with time-varying delay: a PD bumpless transfer control scheme

“…The hidden Markovian model was used by Bai and Zhou (2023) to describe the asynchrony between the original system and the filter, and linear matrix inequalities were applied to implement asynchronous filtering. The problem of robust dynamic output feedback (OF) stabilization was studied for uncertain SMJSs with time-varying by Sun et al (2022). Liang et al (2023) obtained an asynchronous sliding mode control law using event-triggered strategy to ensure the reachability of SMJSs with time-varying delay.…”