Finite-time adaptive robust simultaneous stabilization of nonlinear delay systems by the Hamiltonian function method

Robust simultaneous stabilization of multiple n‐degree‐of‐freedom robot systems

“…Let X 0 ∶= [x T 0 , 𝜉 T 0 ] T . Because of ∇H(x 0 ) = 0, ∇H(𝜉 0 ) = 0, so X 0 is the equilibrium point of the system (26). On the other hand, it is easy to know that H(X) is locally strictly minimal at X 0 .…”

“…As is well known, the Hamiltonian function method is an important one in studying nonlinear system because it has clear physical meaning and successfully solved many important nonlinear problems [21][22][23][24][25][26][27][28][29][30]. Moreover, the generalized Hamiltonian system is a class of open one possessing energy dissipation, energy generation, and energy exchange with external environment, which is a more extensive dynamic system [21].…”

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

“…When it comes to the nonlinear singular system, the finite-time simultaneous stabilization of two nonlinear singular systems and more than two nonlinear singular systems is considered in this study. It is worth noticing that it is also called finite-time stability, i.e., states of the system reach the equilibrium point within a fixed time T and stay at the equilibrium point when t > T [23][24][25][26][27][28][29]. e finite-time robust stabilization problem of general nonlinear time-delay systems is studied based on the Hamiltonian function method and observer design in [26].…”

“…e finite-time robust stabilization problem of general nonlinear time-delay systems is studied based on the Hamiltonian function method and observer design in [26]. In [27], the finitetime stabilization is investigated for a class of singular systems by the constructed new Lyapunov functional, while the finitetime robust simultaneous stabilization and adaptive robust simultaneous stabilization have been investigated for nonlinear systems with time delay in [28,29], respectively.…”

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

“…e finite-time H ∞ controller has been given for the nonlinear singular discretetime system in [40,41] and for the nonlinear singular continuous time system in [42], respectively. It is worth pointing out that there is another definition of finite-time stability, where all states of the system reach the equilibrium point within a fixed time T and stay at the equilibrium point permanently [21,[43][44][45][46][47]. Based on the Hamiltonian function method, the authors in [43] studied the observer design problem of general nonlinear time-delay systems and gave the finite-time robust stabilization results; the authors in [44] investigated the finite-time stabilization problem for a class of singular systems by the constructed new Lyapunov functional while the finite-time robust simultaneous stabilization and adaptive robust simultaneous stabilization have been investigated for nonlinear systems with time delay in [45,46], respectively.…”