Strongly absolute stability of Lur'e descriptor systems: Popov‐type criteria

Abstract

SUMMARYIn this paper, we consider the strongly absolute stability problem of Lur'e descriptor systems (LDSs). First, we define a generalized Lur'e Lyapunov function (GLLF) and show that the negative-definite property of the derivative of the GLLF guarantees strongly absolute stability of LDSs. As a result, the existing Popov-type criteria are reduced to sufficient conditions for the existence of the GLLF. Then, we propose a necessary and sufficient condition for the existence of the GLLF to guarantee the strongly absolute stability of LDSs. This criterion is shown to be less conservative than the existing ones. Finally, we discuss the computational issues and present two numerical examples to illustrate the effectiveness of the obtained results.

Stability and strong passivity of nonlinear descriptor systems

“…In [17], [18], strongly absolute stability problem for LDS is considered. However, the proposed results requires H to be a linear time-invariant descriptor system and nonlinearity belong to [0, K].…”

“…In [15], a sufficient condition for nonlinear descriptor systems to be locally asymptotically stable and of index one is proposed. In [17], [18], strongly absolute stability of Lur'e type descriptor systems is defined to be globally stable and of index one and some criteria are proposed.…”

“…The other class of the existing stability results deal with stability properties of the full state x and are derived by using LFCs relating to the dynamic state and the relationship between the static and dynamic states (see e.g. [14], [15], [16], [17], [18]). Impulse phenomenon which may occur in descriptor systems is undesirable since it will destroy the systems.…”

Stability analysis and control of Lur'e singularly perturbed uncertain systems

“…Considering a class of uncertain Lur'e singular systems with time-delays, sufficient conditions of robust stability are derived and robust H ∞ state feedback controller is developed in [16]. The strongly absolute stability of Lur'e descriptor systems and absolute stability of Lur'e singularly perturbed systems are studied in [17] and [6] respectively.…”

Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

“…The structure of the sector condition in the form of (4) or (5) has been widely considered (see [6,7,26,27] and the references therein). As stated in [9], this sector structure does not involve any approximation of nonlinearities by their norms.…”