Positive 1D and 2D Systems

Kaczorek, Tadeusz

doi:10.1007/978-1-4471-0221-2

Cited by 735 publications

(465 citation statements)

References 0 publications

Supporting

Mentioning

464

Contrasting

Order By: Relevance

“…Continuous-time and discrete-time positive systems have been studied in detail in recent years [1][2][3][4][5][6][7][8][9][10]. If the state and output possess the positivity property under nonnegative initial conditions and controls, the positivity is said to be internal or, simply, the system is positive.…”

Section: Introductionmentioning

confidence: 99%

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

Sen

2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov's inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

Sen

2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…The positive fractional linear systems have been investigated in [6][7][8]. The stability is a basic notion of the analysis of dynamical linear and nonlinear systems [2,[9][10][11]. Stability of fractional linear continuous-time systems has been investigated in the papers [3,12,10,[13][14].…”

Section: Introductionmentioning

confidence: 99%

“…An overview of state of the art in positive systems theory is given in the monographs [1,2] A variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc. Mathematical fundamentals of the fractional calculus are given in the monographs [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

Kaczorek

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. The stability of fractional standard and positive continuous-time linear systems with state matrices in integer and rational powers is addressed. It is shown that the fractional systems are asymptotically stable if and only if the eigenvalues of the state matrices satisfy some conditions imposed on the phases of the eigenvalues. The fractional standard systems are unstable if the state matrices have at least one positive eigenvalue.Key words: stability, fractional, positive, linear, continuous-time, system, integer, rational, order. Stability of fractional positive continuous-time linear systemswith state matrices in integer and rational powers The following notation will be used: ℜ -the set of real numbers, ℜ n×m -the set of n×m real matrices, ℜ + n×m -the set of n×m real matrices with nonnegative entries and ℜ + n = ℜ + n×1 , M n -the set of n×n Metzler matrices (real matrices with nonnegative off-diagonal entries), I n -the n×n identity matrix. PreliminariesConsider the fractional autonomous continuous-time linear system BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. XX, No. Y, 2016 DOI: 10.1515/bpasts-2016 Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

show abstract

“…An overview of the positive realization problem is given in [1,2,6,9]. The realization problem for positive continuous-time and discrete-time linear system has been considered in [6,7,[10][11][12][13][14][15][16][17][18][19][20][21][22] and for linear systems with delays in [6,10,15,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A new approach to the realization problem for fractional discrete-time linear systems

Kaczorek

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

show abstract

Positive 1D and 2D Systems

Cited by 735 publications

References 0 publications

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

A new approach to the realization problem for fractional discrete-time linear systems

Contact Info

Product

Resources

About