Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

Abstract

Summary This paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.

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

“…So-called simultaneous stabilization is to design a single controller to stabilize multiple systems simultaneously. Whether it is for theory or application, simultaneous stabilization problem is all a very challenging research issue [15][16][17][18][19][20].…”

“…In Howitt and Luus [17] and Blondel [18] obtained the simultaneous stabilization results for a set of linear systems. In recent literature [15,16,19,20], the authors developed several simultaneous stabilization results on nonlinear systems. In Cai et al [15], by using the control storage function (CSF), the simultaneous stabilization of a group of typical nonlinear systems was studied, and the corresponding H ∞ controller was designed.…”

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.…”