Impulsive positive observers and dynamic output feedback stabilization of positive linear continuous systems

Xiao, Jiang‐Wen; Hu, Meng‐Jie; Wang, Yan‐Wu; Chen, Wu‐Hua

doi:10.1002/rnc.3685

Cited by 24 publications

(13 citation statements)

References 42 publications

(71 reference statements)

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“…ω ( t ) represents exogenous input signal, which influences the dynamics of the mass of propofol in the central compartment. According to Xiao et al, two unstable subsystems are taken into account and the parameters are given

\begin{matrix} alignleft \\ align-1 k_{11}^{1} & align-2 = 4.5, k_{21}^{1} = 0.95, k_{12}^{1} = 0.3, k_{22}^{1} = - 2.75, b_{1}^{1} = 1.5, \\ align-1 d_{1}^{1} & align-2 = 0.25, k_{11}^{2} = - 2.85, k_{12}^{2} = 0.75, k_{22}^{2} = 4, k_{21}^{2} = 0.2, \\ align-1 b_{1}^{2} & align-2 = 0.4, d_{1}^{2} = 0.41, g_{1} = 0.15, g_{2} = 0.23, k_{c}^{1} = 0.32, k_{c}^{2} = 0.22 . \end{matrix}

Let μ 1 = μ 2 = 1, μ 12 = −10, and μ 21 = −9 be given. Solving by means of the Linprog Toolbox, we can derive the required controller gain matrices

K_{1} = [\begin{array}{cc} 0.0165 & 0.0021 \end{array}], K_{2} = [\begin{array}{cc}  \end{array}]

…”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Wang

Zhao

2019

Intl J Robust & Nonlinear

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Summary In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.

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\begin{matrix} alignleft \\ align-1 k_{11}^{1} & align-2 = 4.5, k_{21}^{1} = 0.95, k_{12}^{1} = 0.3, k_{22}^{1} = - 2.75, b_{1}^{1} = 1.5, \\ align-1 d_{1}^{1} & align-2 = 0.25, k_{11}^{2} = - 2.85, k_{12}^{2} = 0.75, k_{22}^{2} = 4, k_{21}^{2} = 0.2, \\ align-1 b_{1}^{2} & align-2 = 0.4, d_{1}^{2} = 0.41, g_{1} = 0.15, g_{2} = 0.23, k_{c}^{1} = 0.32, k_{c}^{2} = 0.22 . \end{matrix}

Let μ 1 = μ 2 = 1, μ 12 = −10, and μ 21 = −9 be given. Solving by means of the Linprog Toolbox, we can derive the required controller gain matrices

K_{1} = [\begin{array}{cc} 0.0165 & 0.0021 \end{array}], K_{2} = [\begin{array}{cc}  \end{array}]

…”

Section: Examplementioning

confidence: 99%

“…(t) represents exogenous input signal, which influences the dynamics of the mass of propofol in the central compartment. According to Xiao et al, 43 two unstable subsystems are taken into account and the parameters are given…”

Section: Examplementioning

confidence: 99%

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Wang

Zhao

2019

Intl J Robust & Nonlinear

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“…Also, such an external positivity concept does not imply positivity for all time of the inputoutput energy for eventually negative controls. See, for instance, [31][32][33] and some references therein.…”

Section: A Rational Functionĥ( ) Of the Complex Variable Ofmentioning

confidence: 99%

On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems

Sen

2017

Discrete Dynamics in Nature and Society

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This paper investigates some parallel relations between the operators ( − ) and in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by -operators, and their parallel interpretations as pseudocontractive properties of their counterpart ( − )-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals.

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“…Recently, stability problems of impulsive switched systems have been studied in other works . Moreover, there are also some results in the framework of positive systems . Particularly, Wang et al addressed the exponential stability problem of continuous‐time impulsive positive (nonswitched) systems with mixed time‐varying delays.…”

Section: Introductionmentioning

confidence: 99%

“…[33][34][35] Moreover, there are also some results in the framework of positive systems. [36][37][38][39] Particularly, Wang et al 36 addressed the exponential stability problem of continuous-time impulsive positive (nonswitched) systems with mixed time-varying delays. In addition, Li and Xiang 40 studied the problems of exponential stability and L 1 -gain control for continuous-time positive impulsive switched systems with mixed time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

Liu

Zhang

Lü

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results.

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Impulsive positive observers and dynamic output feedback stabilization of positive linear continuous systems

Cited by 24 publications

References 42 publications

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

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