Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

Abstract

This paper considers the guaranteed cost finite-time control for positive switched linear systems with time-varying delays. The definition of guaranteed cost finite-time boundedness is firstly given. Then, by using the mode-dependent average dwell time approach, a static output feedback law and a state feedback control law are constructed, respectively, and sufficient conditions are obtained to guarantee that the closed-loop system is guaranteed cost finite-time boundedness. Such conditions can be easily solved by linear programming. Finally, an example is given to illustrate the effectiveness of the proposed method.

Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

“…It should be noted that the proposed cost function is different from the nonpositive systems [24][25][26]. Particularly, if = 1, this definition is turned into the definition of cost function in positive switched system [27]. This proposed definition provides a more useful description, because it takes full advantage of the characteristics of nonnegative states of FOPSS.…”

“…It has the advantage of providing an upper bound on a given system performance index and thus the system performance degradation incurred by the uncertainties or time delays is guaranteed to be less than this bound [24,25]. So it is necessary to study the design problem of guaranteed cost finite-time controller [26,27]. In [26], robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay was considered.…”

“…In [26], robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay was considered. In [27], guaranteed cost finite-time control was extended to positive switched linear systems with time-varying delays and a cost function for positive systems (or positive switched systems) was also proposed. As we know, fractional-order systems have some different features compared with ordinary systems, like the stability criterion.…”

Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

“…In [26], the problem of robust nite-time guaranteed cost control for a class of impulsive switched systems with time-varying delay was studied. Very recently, [27] and [28] considered the guaranteed cost nite-time control for positive switched linear systems, [29] studied the guaranteed cost nite-time control for fractional-order positive switched systems. However, the problem of guaranteed cost nite-time control for positive switched nonlinear systems is still open, because nonlinear system is more complex than the linear system and there is a lack of e ective methods.…”

“…An output feedback controller is designed and some su cient conditions are obtained to guarantee that the closed-loop system is GCFTB. The main contributions lie in two aspects: 1) This system model is more general, so that the systems dealt with in [2,4,5,7,14,19,27,28,30] can be regarded as especial forms of the system. 2) A new nonlinear LyapunovKrasovskii functional is constructed and the obtained conditions can be easily solved by linear programming.…”