Structural properties of positive periodic discrete-time linear systems: canonical forms

Bru, Rafael; Romero, Sergio; Sánchez, Elena

doi:10.1016/s0096-3003(03)00665-9

Cited by 8 publications

(12 citation statements)

References 11 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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“…The so-called system function of a variable network and a bi-frequency system function are used in (Zadeh, 1950) for frequency analysis of variable networks. A state space model with time-varying coefficients is usually in use to describe linear time-varying (LTV) systems universally, e.g., (Kaczorek, 2001;Bru et al, 2004). A discrete time domain state space model, transition matrices and pseudo-modal parameters are used to describe and identify LTV systems in (Liu, 1997;1999;Liu and Deng, 2005).…”

mentioning

confidence: 99%

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

Kłosiński

2009

International Journal of Applied Mathematics and Computer Science

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The main subject of the paper is the description and determination of the impedance operator of a linear periodically timevarying (LPTV) one-port network in the steady-state. If the one-port network parameters and the supply vary periodically with the same period, the network reaches a periodic steady state. However, the sinusoidal supply may induce a nonsinusoidal voltage or current. It is impossible to describe such a phenomenon by means of one complex number. A periodically time-varying one-port network working in a steady-state regime can be described with a circular parametric operator. Within the domain of discrete time, such an operator takes the form of a matrix with real-valued entries. The circular parametric operator can be transformed into the frequency domain using a two-dimensional DFT. This description makes it possible to quantitatively assess LPTV system input and output harmonics aliasing. The paper also presents the derivation and the proof of convergence of an iteration scheme for the identification of circular parametric operators. The scheme may be used to determine the impedance of an LPTV one-port network. Some results of computer simulations are shown.

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Input–output gain analysis of positive periodic systems

Zhu

Lam

Ebihara

2021

Intl J Robust & Nonlinear

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This paper investigates the input‐output gains, including ℓ1‐ and ℓ∞‐gains and L1‐ and L∞‐gains, of discrete‐time and continuous‐time positive periodic systems. For the discrete‐time case, the input–output gain can be characterized by linear inequalities. For the continuous‐time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1‐ (L1‐) gain of discrete‐time (continuous‐time) positive periodic systems is equivalent to the of ℓ∞‐ (L∞‐) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.

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Structural properties of positive periodic discrete-time linear systems: canonical forms

Cited by 8 publications

References 11 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

The steady-state impedance operator of a linear periodically time-varying one-port network and its determination

Input–output gain analysis of positive periodic systems

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