Canonical forms for positive discrete-time linear control systems

Bru, Rafael; Romero, Sergio; Sánchez, Elena

doi:10.1016/s0024-3795(00)00044-6

Cited by 47 publications

(34 citation statements)

References 9 publications

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“…Similarly, the system is said to be internally nonnegative/positive (or, via an abbreviate notation, as nonnegative/positive) if both state and output trajectories are everywhere nonnegative/positive for any nonnegative/positive input [3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, throughout this paper, the nonnegativity/positivity properties are referred to as internal (external) if they refer to the state (output) trajectory under nonnegative/positive input while no specification internal/external is given if both state and output trajectories exhibit the corresponding property.…”

Section: Assertion 45 If Assumptions 42-43 Hold and K Is Either Bmentioning

confidence: 99%

“…Positive systems have an important relevance since the input, state, and output signals in many physical or biological systems are necessarily positive [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Therefore, important attention has been paid to such systems in the last decades.…”

Section: Introductionmentioning

confidence: 99%

“…However, hyperstable systems of second and higher orders are not guaranteed to be externally positive since the impulse response kernel matrix is 2 Journal of Inequalities and Applications everywhere positive definite but not necessarily positive [19]. The properties of those systems like, for instance, stability, controllability/reachability or pole assignment through feedback become more difficult to analyze than in standard systems because those properties have to be simultaneously compatible with the nonnegativity/positivity concepts (see, e.g., [7][8][9][10][11][12][13]18]). Nonnegativity/positivity properties apply for both continuoustime and discrete-time systems and are commonly formulated on the first orthant which is an important case in applications [7-15, 18, 20].…”

Section: Introductionmentioning

confidence: 99%

“…Also, eigenvalue regions for discrete and continuous-time positive linear systems have been obtained in [13] by using available information on the main diagonal entries of the system matrix while the absolute stability of discrete-time positive systems has been investigated in [17] when subject to unknown nonlinearities within a class of differential constraints with related positivity properties. Also, the properties of controllability and reachability as well as the stability of positive systems using 2D discrete state-space models and graph theoretic formalisms have been studied in the literature (see, e.g., [7,9,10,12,20,21]). The reachability and controllability as well as the related pole-assignment problem have been also exhaustively investigated for continuous-time positive systems (see, e.g., [7,13,[22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays

Sen

2007

J. Inequal. Appl.

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This paper discusses nonnegativity and positivity concepts and related properties for the state and output trajectory solutions of dynamic linear time-invariant systems described by functional differential equations subject to point time delays. The various nonnegativities and positivities are introduced hierarchically from the weakest one to the strongest one while separating the corresponding properties when applied to the state space or to the output space as well as for the zero-initial state or zero-input responses. The formulation is first developed by defining cones for the input, state and output spaces of the dynamic system, and then extended, in particular, to cones being the three first orthants each being of the corresponding dimension of the input, state, and output spaces.

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Section: Assertion 45 If Assumptions 42-43 Hold and K Is Either Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays

Sen

2007

J. Inequal. Appl.

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“…Positive reachability of linear positive systems has been studied since 1980's both for discrete-and continuous-time systems [1][2][3][4][5][6][7][8][9][10][11]. The results show that there is a significant difference between discrete-time and continuous-time systems with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

On positive reachability of time-variant linear systems on time scales

Bartosiewicz¹

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. Positive reachability of time-variant linear positive systems on arbitrary time scales is studied. It is shown that the system is positively reachable if and only if a modified Gram matrix corresponding to the system is monomial. The general criterion is then specified for particular cases of continuous-time systems and various classes of discrete-time systems. It is shown that in the case of continuous-time systems with analytic coefficients the conditions for positive reachability are very restrictive, similarly as for time-invariant systems.

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Improved Controller Design for Uncertain Positive Systems and its Extension to Uncertain Positive Switched Systems

Zhang

Zhao

Zhang

et al. 2017

Asian Journal of Control

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This paper is concerned with the controller design of uncertain positive systems. First, we decompose the feedback gain matrix K m×n into m × n non-negative components and m × n non-positive components. For the non-negative components, each component contains only one positive element and the other elements are zero. Similarly, each non-positive component contains only one negative element and the other ones are zero. Then, a simple and effective controller design approach of uncertain positive systems is proposed by incorporating the decomposed feedback gain matrix into the resulting closed-loop systems and further applied to uncertain positive switched systems. It is shown that the designed controller is less conservative compared with those in the literature. Finally, a numerical example is provided to verify the validity of the proposed design.

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Canonical forms for positive discrete-time linear control systems

Cited by 47 publications

References 9 publications

About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays

About K-Positivity Properties of Time-Invariant Linear Systems Subject to Point Delays

On positive reachability of time-variant linear systems on time scales

Improved Controller Design for Uncertain Positive Systems and its Extension to Uncertain Positive Switched Systems

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