Sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and application to H∞ filtering for linear systems with time-varying delays

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109390
Author(s):  
Xian-Ming Zhang ◽  
Qing-Long Han ◽  
Xiaohua Ge
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Closed Intervals ◽  
Polynomial Inequalities

scholarly journals Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangyang Cao ◽  
Leipo Liu ◽  
Zhumu Fu ◽  
Xiaona Song ◽  
Shuzhong Song
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
State Feedback Control ◽  
Time Varying ◽  
Switched Linear Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Finite Time Boundedness

This paper considers the guaranteed cost finite-time control for positive switched linear systems with time-varying delays. The definition of guaranteed cost finite-time boundedness is firstly given. Then, by using the mode-dependent average dwell time approach, a static output feedback law and a state feedback control law are constructed, respectively, and sufficient conditions are obtained to guarantee that the closed-loop system is guaranteed cost finite-time boundedness. Such conditions can be easily solved by linear programming. Finally, an example is given to illustrate the effectiveness of the proposed method.

scholarly journals Positive time-varying continuous-time linear systems and electrical circuits

2015 ◽  
Vol 63 (4) ◽  
pp. 837-842 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Large Class ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Electrical Circuits ◽  
Time Varying Parameters ◽  
Positive Time ◽  
Necessary And Sufficient ◽  
Time Linear

AbstractThe positivity of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the systems and electrical circuits are established. It is shown that there exists a large class of positive electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

scholarly journals Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 17-20
Author(s):  
Tadeusz Kaczorek ◽  
Łukasz Sajewski
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Positive Time

The global stability of positive  discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.

Exponential Stability for Grey Linear Systems with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 2258-2262
Author(s):  
Ji Chao Wang ◽  
Li Jun Song ◽  
Wei Liu ◽  
Jin Fang Han
Keyword(s):  
Exponential Stability ◽  
Linear Systems ◽  
Stability Problem ◽  
Measure Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Matrix Measure ◽  
Time Varying Delay ◽  
The Matrix ◽  
Varying Delay

In this paper, the exponential stability problem of grey linear systems with time-varying delay is investigated. By using the matrix measure theory and differential inequality approach, some practical sufficient conditions for guaranteeing the exponential stability of the grey linear systems with time-varying delay are presented. The grey-matrix measure and norm are also introduced.

scholarly journals Positivity and stability of fractional descriptor time–varying discrete–time linear systems

2016 ◽  
Vol 26 (1) ◽  
pp. 5-13 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Varying ◽  
Fractional Systems ◽  
Kronecker Theorem ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor time-varying discrete-time linear systems. A method for computing solutions of fractional systems is proposed. Necessary and sufficient conditions for the positivity of these systems are established.

On the Stability of Second Order Time Varying Linear Systems

2005 ◽  
Vol 128 (3) ◽  
pp. 408-410 ◽  
Author(s):  
M. Tadi
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Stiffness Matrix ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Time Varying ◽  
The Stability ◽  
Second Order Systems

This note considers the stability of linear time varying second order systems. It studies the case where the stiffness matrix is a function of time. It provides sufficient conditions for stability and asymptotic stability of the system provided that certain conditions on the stiffness matrix are satisfied.

scholarly journals Minimum Energy Control Of Positive Time-Varying Linear Systems

2015 ◽  
Vol 9 (4) ◽  
pp. 225-228 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Time Varying ◽  
Energy Control ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Positive Time

AbstractThe minimum energy control problem for the positive time-varying linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.

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