Observer‐based H_∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Abstract

Summary This paper addresses the observer‐based H∞ control of Markovian jump systems with interval time‐varying delays and incomplete transition rates. To reduce the conservatism of proposed results, a modified Lyapunov‐Krasovskii functional is constructed, where an improved delay partitioning method is used by partitioning the delay interval into multiple segments with a geometric sequence. Moreover, the Jensen‐based integral inequality and the reciprocally convex technique are used to tackle the time‐varying delays. Some less conservative stochastic stability criteria are derived in the framework of linear matrix inequalities. Then, the observer‐based H∞ controller is designed. Finally, three numerical examples are given to demonstrate the merit and effectiveness of the proposed method.

Observer-based H∞ control for uncertain one-sided Lipschitz Markovian jump-delayed systems with partially unknown transition rates

“…Example 2: A single-link robot arm is considered, in which the system model is constructed as follows (Shu et al, 2018)…”

“…He also studied the problem of robust controller design for finite-time uncertain OSL systems and uncertain quasi OSL systems. Shu et al (2018) studied observer-based H ∞ control for a class of MJSs with time-varying delay and incomplete transition rate using a new time-delay partitioning method. However, the method is not applicable when considering nonlinear functions.…”

“…A special transformation of LMIs can provide less conservatism. Shu et al (2018) for a class of linear systems, the observer-based H ∞ control problem of MJSs with interval time-varying delay and incomplete transfer rate is studied. An improved Lyapunov–Krasovskii functional is constructed, in which an improved delay partition method is used to effectively reduce the conservatism.…”

H∞ Control design for discrete‐time nonlinear delayed systems

“…Specifically, $$$ {H}_{\infty } $$$ controllers are used mainly in the control theory to synthesize controllers to reach stabilization with guaranteed performance 27,28 . Besides, the $$$ {H}_{\infty } $$$ method has the reward over the existing control systems, in that they are promptly suitable for problems which are connecting delayed dynamical systems with cross‐combination between transmission signals 29‐31 . Also, Lee et al 32 studied the nonlinear delayed dynamical systems via single quadratic LKF by using robust control.…”

“…27,28 Besides, the H ∞ method has the reward over the existing control systems, in that they are promptly suitable for problems which are connecting delayed dynamical systems with cross-combination between transmission signals. [29][30][31] Also, Lee et al 32 studied the nonlinear delayed dynamical systems via single quadratic LKF by using robust control. Especially, Koo et al 11 discussed the nonlinear delayed system with reliable fuzzy control.…”