scholarly journals Discrete Lyapunov function by means of a discrete residual energy function and stability analysis for discrete time physical systems

2021 ◽  
Author(s):  
Cem Civelek
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Dynamic System ◽  
Discrete Time ◽  
Energy Function ◽  
Residual Energy ◽  
Discrete Time System ◽  
Dissipation Energy ◽  
Physical Systems ◽  
D Model

In this research paper beginning from the fundamental concepts, all the basic approach is introduced for short. Then after obtaining the discrete Lagrange-dissipative model ({L,D}- model for short) of a discrete time observed physical/engineering dynamic system, the model will be used to develope the discrete Hamiltonian together with discrete dissipation energy as discrete Lyapunov function and as such, a systematic method is proposed to obtain discrete Lyapunov function in form of a residual energy function for discrete (time) observed physical systems to analyze the discrete time system related to stability. Stability analysis of a discrete time observed physical dynamic system is performed using discrete Lyapunov function in form of a residual energy function consisting of Hamiltonian together with dissipation energy. Application of the method was shown using two discrete time physical examples, one of which is a coupled one and time dependent. This coupled physical discrete time example is analyzed related to stability using two different formulations, one form of which leads to a result.

Observability, controllability and stability analysis of discrete time engineering dynamic systems by means of Lagrangian, Hamiltonian and dissipative functions in discrete forms

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Cem Civelek
Keyword(s):  
Stability Analysis ◽  
Dynamic System ◽  
Discrete Time ◽  
Dissipation Function ◽  
Dissipative Function ◽  
Engineering System ◽  
Variable Theory ◽  
Content Type ◽  
Discrete Equations ◽  
D Model

Purpose The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types. Design/methodology/approach An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function. Findings The related analysis can be carried out easily depending on the values of classical elements. Originality/value Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

Stability analysis of a discrete-time system with a variable-, fractional-order controller

2010 ◽  
Vol 58 (4) ◽  
pp. 613-619 ◽  
Author(s):  
P. Ostalczyk
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Discrete Time System ◽  
Time System ◽  
Matrix Condition Number ◽  
Fractional Order Controller ◽  
Matrix Condition

Stability analysis of a discrete-time system with a variable-, fractional-order controllerVariable, fractional-order backward difference is a generalisation of commonly known difference or sum. Equations with these differences can be used to describe a variable-, fractional order digital control strategies. One should mention, that classical tools such as a state-space description and discrete transfer function cannot be used in the analysis and synthesis of such a type of systems. Equations describing a closed-loop system are proposed. They contain square matrices imitating the action of matrices in the system polynomial matrix description. This paper focuses on the stability analysis of a closed-loop SISO linear system with a controller described by the equations mentioned. A stability condition based on a transient denominator matrix condition number is proposed. Investigations are supported by two numerical examples.

Exponential Stability Analysis of Fixed Point Interfered Nonlinear Digital Systems in the Presence of Quantization and Overflow Constraints

2020 ◽  
Vol 19 (04) ◽  
pp. 2050040
Author(s):  
Saddam Hussain Malik ◽  
Muhammad Tufail ◽  
Muhammad Rehan ◽  
Shakeel Ahmed
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Digital Systems ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Digital Hardware ◽  
Time Systems

Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.

scholarly journals Partitioning Technique for Relaxed Stability Criteria of Discrete-Time Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Kuang-Yow Lian ◽  
Wen-Tsung Yang ◽  
Peter Liu
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Discrete Time System ◽  
Interval Time ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Varying Delay

We demonstrate an improved stability analysis based on a partition oriented technique for discrete-time systems with interval time-varying delay. The partition oriented technique introduces beneficial terms contributing to the negative definiteness of the Lyapunov function difference, meanwhile completely avoiding traditional inequality based approaches. In contrast, nonpartitioning oriented techniques do not put emphasis on further dividing the interval of the summation in the Lyapunov function. Herein, we demonstrate that the advantages of exploiting partitioning techniques manifest the relaxed stability criteria, as well as the flexibility to tune tradeoff between allowable timedelay range performance and computational load. Simulation carried out on a benchmark discrete-time system reveals the significant improvement in terms of maximum allowable upper bound in comparison.

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