Output feedback strict passivity of discrete-time nonlinear systems and adaptive control system design with a PFC

Output tracking control of discrete-time nonlinear systems by adaptive PID based on output feedback passivity

“…Output feedback strict passivity and strong output feedback strict passivity for the system (4) is defined as follows [9], [17]:…”

“…Remark 1: Sufficient conditions for the system (4) to be OFSP with a following 2 positive definite function has been provided as follows [9], [17]: C1) The system has relative degree of 0 and ( ( )) > 0, ∀ ( ). C2) The zero dynamics of the system:…”

“…Under Assumption 3, for a strong OFSP augmented system (17), there exists an ideal static output feedback:…”

“…For discrete-time nonlinear systems, passivity properties and passivity based control have recently been investigating with a great deal of attention [6], [7], [8], [9], [10]. One of the most attractive conditions for the passivity based control is 'output feedback strictly (exponentially) passive(OFSP or OFEP)' condition [4], [5], [9], [10]. The system is said to be OFSP if there exists an output feedback such that the resulting closed loop system is strictly passive.…”

ASPR based adaptive output feedback control system design via T-S fuzzy model for nonlinear systems

“…In such a case, one has to design a *This work was partially supported by KAKENHI, the Grant-in-Aid for Scientific Research (C) 25420444, from the Japan Society for the Promotion of Science (JSPS PFC based on a nonlinear model and/or parameter varying model. For nonlinear systems, the equivalent condition of the ASPR-ness for linear system is replaced with the output feedback exponential passivity (OFEP) [9], [10], and thus if a PFC which renders the augmented system OFEP can be designed for nonlinear systems, one can easily obtain a stable adaptive output feedback control system for nonlinear systems [9], [10], [11]. Unfortunately, only a few concrete design schemes of the PFC for nonlinear systems have been proposed [7], [12].…”