Lyapunov exponents for systems with unbounded coefficients

Abstract. The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

show abstract

“…Some further results in this direction contains [64]. Paper [65] deals with the case of unbounded set D.…”

Section: Definitionmentioning

confidence: 99%

Stability and controllability of switched systems

Klamka¹,

Czornik²,

Niezabitowski³

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

View full text Add to dashboard Cite

show abstract

“…Models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc. The Lyapunov, Perron and Bohl exponents and stability of time-varying discretetime linear systems have been investigated in [1][2][3][4][5][6][7][8][9]. The positive standard and descriptor systems, and their stability have been analyzed in [13][14][15][16].…”

mentioning

confidence: 99%

Positivity and Stability of Time-Varying Discrete-Time Linear Systems

Kaczorek

2015

Intelligent Information and Database Systems

View full text Add to dashboard Cite

IntroductionA dynamical system is called positive if its trajectory starting from any nonnegative initial condition state remains forever in the positive orthant for all nonnegative inputs. An overview of state of the art in positive system theory is given in the monographs [7,10] and in the papers [11][12][13][14]. Models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc. The Lyapunov, Perron and Bohl exponents and stability of time-varying discretetime linear systems have been investigated in [1][2][3][4][5][6][7][8][9]. The positive standard and descriptor systems, and their stability have been analyzed in [13][14][15][16]. The positive linear systems with different fractional orders have been addressed in [14,17] and the singular discrete-time linear systems in [15].In this paper the positivity and asymptotic stability of the time-varying discretetime linear systems will be investigated.The paper is organized as follows. In section 2 the solution of the state-equation describing the time-varying discrete-time linear system is derived and necessary and sufficient conditions for the positivity of the systems are established. The asymptotic stability of the positive systems is addressed in section 3, where conditions for the stability are proposed. Concluding remarks are given in section 4.The following notation will be used:-the set of real numbers, -the set of real matrices, -the set of matrices with nonnegative entries and , -the identity matrix.

show abstract

“…The Lyapunov, Bohl and Perron exponents and stability of time-varying discrete-time linear systems have been investigated in [3][4][5][6][7][8]. The positivity and stability of fractional time varying discrete-time linear systems have been addressed in [9][10][11][12][13] and the stability of continuous-time linear systems with delays in [14].…”

Section: Introductionmentioning

confidence: 99%