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

Abstract

This study addresses the problems of finite-time simultaneous stabilization for two nonlinear singular systems and more than two nonlinear singular systems. First, we design a suitable output feedback controller and combine the two nonlinear singular systems to generate an augmented system by using an augmented technique. Based on a sufficient condition of the augmented system impulse-free, an important result, that is, the augmented system is finite-time stabilization is presented. Then, the finite-time stabilization problem of more than two singular systems is investigated by dividing the N systems into two sets. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed finite-time stabilization controller for two nonlinear singular systems.

Finite‐time robust simultaneous stabilization control for two nonlinear singular time‐delay systems

“…Apart from the infinite-time control results mentioned in the above literature, the finite-time control one has faster convergence speed, better robustness, and disturbance rejection characteristics [18][19][20]. Tang et al studied the problem of finite-time simultaneous stabilization of a group of stochastic port-controlled Hamiltonian (PCH) systems, and a new control scheme was proposed [18].…”

“…It has clear structure and physical meaning, which plays an important role in stability analysis and stabilization control of the system [21]. In recent years, the method of generalized Hamiltonian system has received more and more attention in nonlinear control theory and application [20], and based on the Hamiltonian method, one has successfully solved many problems of nonlinear systems such as nonlinear time-delay systems and nonlinear singular (time delay) systems [19][20][21][22][23][24][25]. Even so, the above-mentioned literature developed some infinite-time robust stabilization results based on linearization method for the single system; there are few results on the simultaneous stability of the general nonlinear singular systems with time delay, which motivated the present paper.…”

“…Tang et al studied the problem of finite-time simultaneous stabilization of a group of stochastic port-controlled Hamiltonian (PCH) systems, and a new control scheme was proposed [18]. Sun and Li [19] designed a suitable finite-time output feedback controller for multiple nonlinear singular systems. Li et al studied the finite-time simultaneous stability of two nonlinear singular systems with actuator saturation by designing an output feedback controller in [20].…”

“…Its emergence and development have a profound physical background. The generalized Hamiltonian system describes a wider open system with energy exchange, energy dissipation, and energy generation of the external environment [19]. It has clear structure and physical meaning, which plays an important role in stability analysis and stabilization control of the system [21].…”