Reliable finite‐time H_∞ control for singular Markovian jump system with actuator saturation via sliding‐mode approach

Abstract

Summary This paper explores the finite‐time H∞ control problem for singular stochastic systems with actuator saturation and time‐varying state delay through the sliding‐mode approach. Time delay is a kind of positive differentiable bounded delay. A novel suitable switching function and a suitable sliding‐mode control law are given to guarantee that the closed‐loop actuator saturating system is singular stochastic H∞ finite‐time boundedness on the specified sliding surface. Sensor failures are taken into consideration for the error system, and sufficient criteria are provided to ensure the error system is singular stochastic finite‐time boundedness. The gain matrices of sliding‐mode controller and state observer are obtained by solving the corresponding linear matrix inequalities. Finally, simulation examples are given to illustrate the proposed method.

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.…”

Input and output strictly passive $$H_\infty $$ control of continuous switched singular systems

“…In Ma et al (2015), the problem of finite-time H ∞ control for a class of discrete-time switched singular time-delay with actuator saturation was studied using the average dwell-time approach. The finite-time H ∞ control problem for singular stochastic systems with actuator saturation and time-varying state delay was studied through the sliding-mode approach in Ma et al (2018). The finite-time H ∞ static output-feedback control problem for a class of discrete-time switched singular time-delay systems subject to actuator saturation was investigated by using the multiple Lyapunov-like function method and the average dwell-time concept of switching signal in Ma and Fu (2016).…”