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A matrix form representation of discrete analogs of various forms of fractional differentiation and fractional integration is suggested. The suggested approach is new, and it can be used in all fields related to fractional-order dynamical systems and fractional-order control, including development of algorithms and software for real-time control, PIλDμ controllers, and modelling and simulation of...
This paper proves the requirement of a time-varying initialization for fractional differential equations. This then requires a new definition for the fractional differintegral that includes the initialization and a new form of the Laplace transform of the fractional differintegral. An initialized fractional system theory is developed.
The aim of this paper is to investigate some properties of the solutions of the differential Riccati-type systems arising in control problems for the time-varying linear systems with jumps. A major attention is paid to the stabilising solution of these systems. Necessary and sufficient conditions for the existence of such solution are derived in the time-invariant case.
A problem of dynamical identification of inputs of systems described by ordinary differential equations is considered. Solving algorithms based on the method of control of a model are suggested.
We consider a class of nonlinear time-variant infinite dimensional a class retarded systems governed by functional-differential equations in a Banach space. It is assumed that the linear part of the equations is unbounded variable operator and the nonlinearities satisfy the local Lipschitz conditions. A solution estimate is derived. By virtue ofthat estimate stability conditions are established.
This paper deals with the controller design for the lateral motion of automatic steering of vehicles. The nonlinear models without and with uncertainties are considered. Sliding mode controllers with first order sliding surfaces are proposed for the control of lateral velocity and yaw rate. These controllers are designed directly based on the second order differential equation model which simplifies...
Physical systems are mostly modelled by differential equations together with initial conditions and boundary conditions. For systems showing some kind of ‘memory’ local differential equations are not appropiate. Particularly in the description of damping behaviour of vis-coelastic media, fractional differential equations are suggested instead by many authors. Many of these approaches use ad hoc definitions...
Kuipers' QSIM algorithm for tracking the monotonicity properties of solutions to differential equations has been revisited by Dordan by placing it in a rigorous mathematical framework. The Dordan QSIM algorithm provides the transition laws from one qualitative cell to the others. We take up this idea and revisit it at the light of recent advances in the field of "hybrid systems" and, more...
We discuss an algebraic and computational framework for formally analyzing hybrid systems that attempts to avoid numerical integration by resorting to (algebraically) finding primitives, and inverting and (numerically) evaluating functions when needed. The goal of the paper is to start exploring a little bit deeper into this idea to try to find out (a) a methodology, (b) algebraic and computational...
This paper focuses on forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability result is based on a theorem on invariant manifolds Banach spaces due to Kurzweil and Halanay. The state-space (based on Liapunov-Krasovskii functionals combined with the 5-procedure) approach is considered. An illustrative...
Complex-fractional systems are systems that are governed by a differential equation characterized by complex order fractional derivatives. A new modeling tool is proposed and used to study these systems: complex order state-space representation. The tool results from the extension of the differentiation order, from order 1 to complex order, in the state equation of classical state-space representation:...
Sufficient conditions of the exponential mean-square stability of a linear stochastic hybrid system with multiplicative noises and the random switching rule are derived. A hybrid system with linear stable and unstable parts with stochastic structures is considered. To analyze the exponential mean-square stability the differential equations for the covariance matrices of solutions are used.
This work presents an Extended Kalman Filter (EKF) for estimating the kinetic rates in bioprocesses. The unknown kinetic rates are modeled as the output of a linear system persistently excited. The gain of the filter is designed by the Ricatti differential equation. The stability and convergence are analyzed using Lyapunov functions. To illustrate the application of this observer, the estimation of...
We show how, using differential inclusions and viability theory it is possible to define sliding modes for (feedback) controlled semilinear differential equations in Banach spaces. We then compare this definition with an extended version of the equivalent control method for infinite dimensional systems proposed by V. Utkin and Yu. Orlov. We prove that, if the sliding manifold satisfies suitable regularity...
Decomposition relationships for nonlinear dynamic system operators into state-space based on vector-matrix series are proposed. The representation for a shift operator on trajectories of nonlinear dynamic system through shift operators on trajectories of multidimensional linear dynamic systems was obtained.
Because the implicit Runge-Kutta method is hard to use, in addition, there is the lack of precision analysis for the implicit Runge-Kutta methods, three classic four-stage implicit Runge-Kutta methods are used to compare their calculation accuracy and the sensitivity of calculation step, these results provided reference for the selection of four-stage implicit Runge-Kutta methods.
The standard setting methodologies have been summaries and reported by various researchers. There are two types of standard, which are relative and absolute. Relative standard is appropriate for examination while absolute standard are most appropriate for a test of competence. This method has been implemented in some organization and institution to evaluate their students or employee performances...
The paper presents a mathematical model and a computer program for determining the override parameters of the hydro generator and automatic voltage regulator (AVR) at the full load sudden disconnection: terminal voltage override of the generator, override time of 1,1Ugn, total response time or transient duration. Essentially the method consists in simulating the application of a negative step type...
This paper analyses free vibration frequencies and modes for thickness-shear and thickness-twist vibrations of centrally partially electroded circular AT-cut quartz plate. The elliptical coordinate is introduced for both un electroded and electrode part. Exact solutions of Mathieu equations which are transferred from the two-dimensional scalar differential equation derived by Tiersten and Smythe are...
The problem of robustly stabilizing a nonlinear system is revisited through a re-examination of the separation theorem, whereby a nonlinear system can be stabilized by a combination of an asymptotic observer and a state feedback controller. The main emphasis is on the notion of strict asymptotic observers — asymptotic observers designed to tolerate uncertainty. It is shown that strict asymptotic observers...
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