Improved results on H∞ stability analysis of sampled-data systems via looped-functionals and zero equalities

Novel Equalities for Stability Analysis of Asynchronous Sampled-Data Systems

“…It is thus an important topic to increase a sampling period while maintaining a system stability. Therefore, sampled-data systems with periodic/asynchronous samplings have been extensively researched in the literature [7]- [15]. In the case of periodic samplings, tools for stability analysis and controller synthesis problems have been well established [11].…”

“…However, in the case of asynchronous samplings, there still exist open problems. To deal with the stability analysis of asynchronous sampled-data systems, there have been three approaches according to modelings of a sampled-data system: impulsive models [7], [9], discrete-time systems [8], [10], input-delay systems [12], [13], [15], [16]. Among them, this paper focuses on the input-delay system approaches, where the original sampled-data system is reformulated into a time-delay system with an incremental delay.…”

“…Commonly, a construction of the functional has played key roles in reducing the conservatism of stability criteria, which results in development of many functionals with use of various quadratic functions and integral quadratic functions [13], [15], [21]. Therefore, the time derivative of the looped-functional also contains integral quadratic functions which cannot be directly utilized as stability conditions expressed in terms of linear matrix inequalities (LMIs).…”

“…Therefore, the time derivative of the looped-functional also contains integral quadratic functions which cannot be directly utilized as stability conditions expressed in terms of linear matrix inequalities (LMIs). To derive and relax LMIs guaranteeing the negativity of a derivative of the functional, integral inequalities [17], [20] and zero equalities [12], [13], [15], [18] have been proposed. The zero equalities can be obtained from the relation among system state variables such as a system state x(t), two consecutive sampled states x(t k ),…”

“…According to integrands in integral quadratic functions, upper bounds obtained from the integral inequalities consist of integral state variables or their interval-normalized versions. In the literature [15], [18], it was numerically shown that simultaneously utilizing these two types of integral state variables contributes to reducing the conservatism of stability criteria for time-delay systems. However, due to slack matrices of the zero equalities, which come from the relation between these two types of integral terms, a computational burden increases.…”