# Stability and stable oscillations in discrete time systems

• 283 Pages
• 1.25 MB
• English
by
Gordon & Breach , Amsterdam
Stability -- Mathematical models, Oscillations -- Mathematical models, Discrete-time systems -- Mathematical m
The Physical Object ID Numbers Statement Aristide Halanay & Vladimir Răsvan Series Advances in discrete mathematics and applications -- v. 2 Contributions Răsvan, V Pagination 283 p. ; Open Library OL18116775M ISBN 10 9056996711

Buy Stability and Stable Oscillations in Discrete Time Systems (Advances in Discrete Mathematics and Applications, Volume 2) on FREE SHIPPING on qualified ordersCited by: Stability and Stable Oscillations in Discrete Time Systems - CRC Press Book The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations.

The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications inCited by: The standard discrete-time system () or equivalently () is asymptotically stable if and only if eigenvalues of (Ã +BK) lie in the unit disk .

EIGENVALUE ASSIGNMENT IN. The current state of affairs in stability theory, absolute stability of control systems and stable oscillations of both periodic and almost periodic discrete systems.

Discrete-Time Models Induced by Impulses Occurring in Continous Time Systems 3. Discrete Systems Occourring from Sampled Data Control Systems 4.

Numerical Treatment of Continous-Time Systems II: Stability Theory 5. Linear Discrete Time Systems with Constant Coefficients 6. General Properties of Linear Systems 7.

Stability by the First Approximation 8. We can use this version of the Lyapunov equation to define a condition for stability in discrete-time systems: Lyapunov Stability Theorem (Digital Systems) A digital system with the system matrix A is asymptotically stable if and only if there exists a unique matrix M that satisfies the Lyapunov Equation for every positive definite matrix N.

The research presented in this thesis considers the stability analysis and control of discrete-time systems with delay. The interest in this class of systems has been motivated tradition-ally by sampled-data systems in which a process is sampled periodically and then controlled via a computer.

This paper studies almost sure stability of general n-dimensional nonlinear time-varying discrete-time stochastic systems and presents a criterion based on a numerical result derived from Higham (), which exploits the stabilizing role of noise in discrete-time systems.

As an application of the established results, this paper proposes a. Well-known stability test for continuous-time systems. To determine the stability of the closed-loop system when the open-loop system is given. Can be reformulated to handle discrete-time systems. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics.

In addition, a discrete time system is often represented in the real world systems such as population models and switched systems.

There are several studies on the stability of a discrete time system [2–4, 8–15, 17, 18, 22–24]. Book Condition: Kluwer Academic Publishers; Dordrecht, Hardcover. Hardcover. Near Fine, light wear/scuff marks to boards, tight binding, interior tidy and bright, whited out name on title page, light wear to bottom spine edge, without Dust : Hardcover.

According to Figure 1, we can get that is unstable and and is asymptotically stable. Thus, is -asymptotically stable by Definition Example Consider a second-order predator-prey system with a prey refuge in the following form: where, represent the prey and predator density, parameters and are the intrinsic growth rates of the prey and the predator, respectively.

stability of linear and nonlinear discrete models. 2 Discrete Linear Models Time-discrete models means that the development of the system is observed only at discrete times t0,t1,t2, and not in a continuous time course.

Assume here that tk+1 = tk +h where h > 0 is a constant step. Signal & System: Stable & Unstable Discrete-Time Systems Topics discussed: 1. Stable discrete-time system. Unstable discrete-time system. Example of a stable discrete-time system.

Example. In Tribology Series, Role of dynamic coefficients in stability. The use of Routh-Hurwitz criterion allows us to show the necessary and sufficient conditions to ensure the stability of an operating point.

Some of relations () include only the dynamic coefficients while the critical mass intervenes in two relations; thus, according to the respective values of the dynamic. Abstract: Dual active bridge (DAB) converters have been widely used in distributed power systems and energy storage equipment.

However, the inherent nonlinearity of the DAB converters can cause stability problem, such as output voltage oscillation. In this paper, the dynamic behavior and stability of a digitally controlled DAB converter with a closed-loop controller are studied. Linear Stability Analysis 1 Linear Stability Analysis 2 Review of 13 Stable Oscillations in Science (and Discrete Time Dynamical Systems Discrete Time Logistic Function Sensitive Dependence in the Logistic Model The Cause of Chaos in the Logistic Model Routes to Chaos in the Logistic Model A.

Unstable system shows erratic and extreme behavior. When unstable system is practically implemented then it causes overflow. Solved problem on stability: Determine whether the following discrete time functions are stable or not.

### Details Stability and stable oscillations in discrete time systems PDF

1) y(n) = x(-n) Solution: we have to check the stability of the system by applying bounded input. of linear and nonlinear systems, their stability and bifurcations have been studied. Introduction Any motion that repeats itself after an interval of time is called vibration or oscillation.

The swinging of a pendulum (Fig.1) and the motion of a plucked string are typical examples of vibration. The theory of vibration deals with the study of. In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for linear signals and systems that take inputs.

If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value > such that the signal magnitude never exceeds, that is. Stability Condition of an LTI Discrete-Time System •Example- Consider a causal LTI discrete-time system with an impulse response • For this system • Therefore S system is BIBO stable • If, the system is not BIBO stable ∞ αFile Size: KB.

### Description Stability and stable oscillations in discrete time systems FB2

Linear stability analysis of discrete-time nonlinear systems. Find an equilibrium point of the system you are interested in. Calculate the Jacobian matrix of the system at the equilibrium point.

Calculate the eigenvalues of the Jacobian matrix. If the absolute value of the dominant eigenvalue is. For discrete-time systems, there are no oscillations only if the pole is on the positive real axis. A pole on the negative real axis causes oscillations with maximum frequency.

Consequently, a discrete-time real-valued first-order system can exhibit oscillations if the pole happens to. History. Lyapunov stability is named after Aleksandr Mikhailovich Lyapunov, a Russian mathematician who defended the thesis The General Problem of Stability of Motion at Kharkov University in A.

Lyapunov was a pioneer in successful endeavoring to develop the global approach to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread local. Continuous time.

A homogeneous continuous linear time-invariant system is marginally stable if and only if the real part of every pole in the system's transfer-function is non-positive, one or more poles have zero real part and non-zero imaginary part, and all poles with zero real part are simple roots (i.e.

the poles on the imaginary axis are all distinct from one another). In this paper we investigate an impulsive discrete time system with delay. By using Lyapunov stability theory and a Razumikhin type technique, some new criteria for the exponentially practical stability of impulsive discrete time system with delay are established.

A numerical example is given to show the effectiveness of our theoretical results. T1 - Stability analysis in continuous and discrete time. AU - Besseling, N.C. N1 - / PY - /1/ Y1 - /1/ N2 - The relation between continuous time systems and discrete time systems is the main topic of this research.

A continuous time system can be transformed into a discrete time system using the Cayley transform. Equivalences of Stability Properties for Discrete-Time Nonlinear Systems and extensions Author: Duc Tran y Supervisors: A/Prof.

Christopher M. Kellett y Dr. Bj orn S. Ru er z ySchool of Electrical Engineering and Computer Science z School of Mathematical and. Abstract: This brief is concerned with the stability problem for a class of discrete-time switched systems with unstable subsystems.

By constructing a quasi-time-dependent Lyapunov function, stability analysis criterion for nonlinear switched systems is developed under a designed switching rule in which the fast and slow switching techniques are adopted for unstable and stable subsystems.Lyapunov stability and asymptotical Lyapunov stability refer to any chosen solution of a differential or discrete time equation, and to a periodic solution in particular.with initial conditions x 1 (0) =y 0 and x 2 (0) =y 1.

Since y(t) is of interest, the output equation y(t) =x 1 (t) is alsoadded. These can be written as which are of the general form Here x(t) is a 2×1 vector (a column vector) with elements the two state variables x 1 (t) and x2 (t).It is called the state variable u(t) is the input and y(t) is the output of the system.