Combined H_∞ and anti‐disturbance control for semi‐Markovian jump systems via a nonlinear disturbance observer

Abstract

This paper investigates a combined H ∞ and anti-disturbance control problem for a class of semi-Markovian jump nonlinear systems with constant time delay, and both modeled and unmodeled disturbances. In particular, the modeled disturbance is thought to be produced by a nonlinear exogenous system and is estimated by introducing a mode-dependent nonlinear disturbance observer. The desired controller for the addressed system is then proposed, which consists of two components: (i) state feedback, which ensures the system's stochastic stability by attenuating the unmodeled disturbance; and (ii) disturbance estimate, which compensates for the modeled disturbance effect. Following that, a novel mode-dependent asymmetric Lyapunov-Krasovskii functional is used to derive the sufficient conditions for the existence of the proposed controller and disturbance observer. The developed theoretical results are supported by three numerical examples that demonstrate the utility of the proposed design method.

Resilient and finite‐time H∞$$ {H}_{\infty } $$ control of semi‐Markov jump systems with both upper and lower thresholds of sojourn time

“…Much attention has been paid to the steady-state performance for discussed systems such as 𝜎-error mean-square stability/stochastic stability since it well describes changes of system state responses during an infinite time interval. [17][18][19] Actually, the problem of realizing the transient performance of the systems is also well worth studying and is of great significance in a variety of occasions. 20,21 Especially, in some practical engineering applications, the state responses of the systems will be required to meet certain requirements in a finite period of time, such as not exceeding a given boundary.…”

“…Stability analysis has always been a research hotspot for systems, and SMJSs are no exception. Much attention has been paid to the steady‐state performance for discussed systems such as $$$ \sigma $$$‐error mean‐square stability/stochastic stability since it well describes changes of system state responses during an infinite time interval 17–19 . Actually, the problem of realizing the transient performance of the systems is also well worth studying and is of great significance in a variety of occasions 20,21 .…”