Exponential output tracking control for positive switched linear systems with time-varying delays

Liu, Shilong; Xiang, Zhengrong

doi:10.1016/j.nahs.2013.07.002

Cited by 62 publications

(50 citation statements)

References 33 publications

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“…, n, where ≤ m ≤ m , and f i ( ) = . (1) is transformed to positive switched linear systems, such as [2,4,5,7,14,27,28]; If m = m = , u(t) = and w(t) = , then the system (1) is turned into the model in [30]; If (1) is converted into the model in [19].…”

Section: Assumption 21 the Nonlinear Function F (X) Lies In Sector mentioning

confidence: 99%

“…For a given constant T f and two vectors ς ≻ ρ ≻ , positive switched nonlinear system (4) is said to be FTB with respect to(ς , ρ, T f , ζ, σ(t)), where w(t) satis es (2), if …”

Section: De Nition 27 ([14] Finite-time Boundedness (Ftb))mentioning

confidence: 99%

“…As a special kind of switched systems, the positive switched systems, whose output and state are nonnegative whenever the initial condition and input are nonnegative, have been applied in many practical systems, such as communication networks [1], viral mutation [2], formation ying [3], and so on. Many remarkable results have been presented, see [4][5][6][7][8][9][10][11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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This paper considers the guaranteed cost nite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the de nition of guaranteed cost nite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and su cient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost nite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the e ectiveness of the proposed method.

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Section: Assumption 21 the Nonlinear Function F (X) Lies In Sector mentioning

confidence: 99%

“…For a given constant T f and two vectors ς ≻ ρ ≻ , positive switched nonlinear system (4) is said to be FTB with respect to(ς , ρ, T f , ζ, σ(t)), where w(t) satis es (2), if …”

Section: De Nition 27 ([14] Finite-time Boundedness (Ftb))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2017

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“…Many remarkable results related to positive switched systems have been presented, see [1][2][3][4][5][6] and references therein. These results mentioned above refer to the positive switched systems with integer order derivative.…”

Section: Introductionmentioning

confidence: 99%

Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

Cao¹,

Liu²,

Xing³

2017

IJIRCST

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Abstract-This paper is concerned with the global exponential stability(GES) and stabilization of fractional-order positive switched systems(FOPSS) with average dwell time(ADT). Firstly, the the concept of GES is extended to FOPSS. Then, by constructing copositive Lyapunov functions and using ADT approach, a state feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is globally exponentially stable. Such conditions can be easily solved by linear programming. Finally, an example is given to demonstrate the effectiveness of the proposed method.Index Terms-fractional-order positive switched systems, global exponential stability, average dwell time, linear programming.

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Observer‐based controller of uncertain Switching Positive Linear Systems: A unilaterally tracking scheme

Nojoumian

Zakerzadeh

Ayati

2022

Asian Journal of Control

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This paper deals with designing a unilateral tracking controller for the Switching Positive Linear Systems (SPLSs). Positive systems are widespread, and most biological, economic systems, and so on, with nonnegative variables, belong to this class of systems. System states are assumed partially unmeasurable; thus, a reduced‐order positive switching observer is utilized to improve the closed‐loop system response. Also, interval uncertainty is considered to provide a more practical result. In addition, a unilateral tracking controller is developed in this study. The unilateral tracking controller keeps the system and observer states in the same direction as the reference system and system output. Also, the unilateral tracking method avoids overshoot. System stability is presented in synchronous and asynchronous switching conditions. In asynchronous switching mode, controller switches have a time lag behind the system's switching. The switching time lag in asynchronous mode is assumed unknown with a known upper bound for each subsystem. The closed‐loop system's stability is guaranteed by utilizing multiple Lyapunov functions, and the Mode Dependent Average Dwell Time (MDADT) strategy. The designed unilateral tracking controller is developed to track a reference system. Also, sufficient conditions are provided to guarantee the L1‐gain performance of the closed‐loop system. Finally, an illustrative example is provided to demonstrate the proposed scheme's effectiveness compared with the foremost existing solutions.

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Exponential output tracking control for positive switched linear systems with time-varying delays

Cited by 62 publications

References 33 publications

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

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

Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

Observer‐based controller of uncertain Switching Positive Linear Systems: A unilaterally tracking scheme

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