Finite-time H ∞ control for nonlinear discrete Hamiltonian descriptor systems

Finite-Time Simultaneous Stabilization of a Set of Nonlinear Singular Systems

“…Definition of finite-time stabilization is proposed for the linear system [9,10] and then extended to the linear singular system [11]. Furthermore, the finite-time stabilization is investigated for the nonlinear discrete-time Hamiltonian singular system [12]. Finite-time stabilization, which is different from asymptotic stability [13][14][15][16][17], is used to describe that the state does not exceed a certain bound during a fixed finite-time interval.…”

Finite-Time H ∞ Control of Affine Nonlinear Singular Systems Subject to Actuator Saturation

“…Unlike the asymptotical stability [23][24][25][26], the finite-time stable (FTS) is that the state (weighted) norm does not exceed a certain boundary within a fixed time T. In many practical applications, FTS plays an important role, such as analyzing the transient behavior of the controlled system within a finite interval. Due to its extensive engineering application background, the FTS problem has attracted much scholarly interest [6,7,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. In [27,28], the FTS problem of the linear system has been investigated.…”

Finite‐time stabilisation for a class of nonlinear descriptor systems

“…In [24], three sufficient conditions of finite‐time stability have been proposed for impulsive switched linear time‐varying systems using function‐dependent dwell time methods. It should be pointed out that there are few results on the finite‐time stabilisation problem of the NDS [25–27]. In [25], the finite‐time control problem has been considered for the nonlinear discrete Hamiltonian descriptor system with a proper state‐feedback by the decomposing system state.…”

“…It should be pointed out that there are few results on the finite‐time stabilisation problem of the NDS [25–27]. In [25], the finite‐time control problem has been considered for the nonlinear discrete Hamiltonian descriptor system with a proper state‐feedback by the decomposing system state. For the nonlinear descriptor systems with interval time varying delay, the finite‐time robust stability has been studied by using the Lyapunov–Krasovskii functional method and descriptor analysis technique in [26].…”

“…In recent years, many effective controllers have been designed by using the Hamiltonian function method [15, 25, 28–32]. Motivated by the Hamiltonian function method, we establish a dissipative matrix method to study the asymptotic stabilisation problem of the NDS [17].…”