Model reduction for discrete-time switched linear time-delayed systems with finite-frequency specifications

2022 ◽  
pp. 014233122110655
Author(s):  
Liankun Sun ◽  
Haiyao Ma ◽  
Zhangang Wang
Keyword(s):  
Model Reduction ◽  
Discrete Time ◽  
Performance Index ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Finite Frequency ◽  
Delayed Systems ◽  
Variable Parameters ◽  
Numerical Examples ◽  
Improve Approximation

The paper focusses on the model reduction of discrete-time switched linear systems with finite-frequency specifications. First, we propose a performance index that can estimate systematic performance over finite frequency. And then, we use GKYP (generalized Kalman–Yakubovich–Popov lemma) and introduce some relaxation matrices with variable parameters to analyse the problem in different situations. Based on the above conditions, sufficient conditions can be obtained for meeting the index of finite frequency. Finally, we illustrate two numerical examples. The results show that the proposed method can improve approximation performance.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

scholarly journals Positive 2D Discrete-Time Linear Lyapunov Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Przemysław Przyborowski ◽  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

scholarly journals Positive Partial Realization Problem for Linear Discrete-Time Systems

2007 ◽  
Vol 17 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Realization Problem ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems

Positive Partial Realization Problem for Linear Discrete-Time SystemsA partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

H∞ model reduction of discrete-time 2D T-S fuzzy systems in finite frequency ranges

2021 ◽  
Vol 37 (1) ◽  
pp. 22
Author(s):  
Ismail Boumhidi ◽  
Abderrahim El Amrani ◽  
Ahmed El Hajjaji ◽  
Bensalem Boukili
Keyword(s):  
Model Reduction ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Finite Frequency

scholarly journals Robust Filtering for Discrete-Time Linear Parameter-Varying Descriptor Systems

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1871 ◽  
Author(s):  
Carlos Rodriguez ◽  
Karina A. Barbosa ◽  
Daniel Coutinho
Keyword(s):  
Discrete Time ◽  
Filter Design ◽  
Linear Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Time Linear

This paper deals with robust state estimation for discrete-time, linear parameter varying (LPV) descriptor systems. It is assumed that all the system state-space matrices are affine functions of the uncertain parameters and both the parameters and their variations are bounded functions of time with known minimum and maximum values. First, necessary and sufficient conditions are proposed for admissibility and bounded realness for discrete linear time-varying (DLTV) descriptor systems. Next, two convex optimisation based methods are proposed for designing admissible stationary linear descriptor filters for LPV descriptor systems which ensure a prescribed upper bound on the ℓ2-induced gain from the noise signal to the estimation error regardless of model uncertainties. The proposed filter design results were based on parameter-dependent generalised Lyapunov functions, and full-order, augmented-order and reduced-order filters were considered. Numerical examples are presented to show the effectiveness of the proposed filtering scheme. In particular, the proposed approach was used to estimate the state variables of a controlled horizontal 2-DOF robotic manipulator based on noisy measurements.

scholarly journals Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition

2016 ◽  
Vol 26 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Performance Index ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.

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