... i=n (t − ts )(i−n)α(3:27) ((i − n)α + 1) 3.3 Linear control system in the general state space form Consider a controllable linear fractional control system of the form : (C Dαs + x)(t) = Ax + bu, ... = ts yields z(ts) = zs, and for t = tf gives z(tf) = zf 2.2 Linear control system in the form of na-integrator Consider a control system of order na, for
... suggested for investigating the asymptotic stability of neutral nonlinear systems The investigation of nonlinear neutral delayed systems with two time dependent bounded delays in to determine the ... function v x xT Hx has been used to investigate the stability of systems 1.1 in see as well The stability of linear neutral systems of type 1.1 , but with different delays h1 and h2 , is studied ... λmin H 2.5 The following lemma gives a representation of the linear neutral system 1.1 on an interval m − τ, mτ in terms of a delayed system derived by an iterative process We will adopt the where...
... the secondorder systems 1.1 , see In this paper, we use this kind of condition to consider the existence of periodic solutions of first-order linear Hamiltonian system with a nonlinear perturbation ... Hamiltonian system 1.5 has at least one 2π-periodic solution Theorem 1.2 Assume that the linear problem 1.14 has only the trivial 2π-periodic solution u and the condition G2 holds Then the Hamiltonian system ... differenziali ordinarie quasilineari condizioni lineari,” Annali di Matematica Pura ed Applicata Serie Quarta, vol 57, pp 49–61, 1962 12 I T Kiguradze, “Boundary value problems for systems of ordinary...
... Example (water tank mixing system) Consider a water tank system that accepts two different water temperatures, while simultaneously throws off the mixed water [18] This system is described by ⎡ ⎢ ... Z You, and E Song, “An efficient algorithm for optimal linear estimation fusion in distributed multisensory systems,” IEEE Transactions on Systems, Man, and Cybernetics, vol 36, no 5, pp 1000–1009, ... Aerospace and Electronic Systems, vol 26, no 6, pp 1011–1021, 1990 [13] W H Kwon, P S Kim, and P Park, “A receding horizon Kalman FIR filter for linear continuous-time systems,” IEEE [14] [15]...
... 3, pp 295–302, 1985 B Aulbach and S Hilger, Linear dynamic processes with inhomogeneous time scale,” in Nonlinear Dynamics and Quantum Dynamical Systems (Gaussig, 1990), vol 59 of Mathematical ... Mathematics, vol 18, no 1-2, pp 18–56, 1990 12 G Hovhannisyan, “Asymptotic stability for 2×2 linear dynamic systems on time scales,” International Journal of Difference Equations, vol 2, no 1, pp 105–121, ... 0, and from 1.24 ζ1 a12 Δ μa12 ζ1 ζ0 − a11 εζ1 a12 Δ 1.30 Gro Hovhannisyan Example 1.3 Consider system 1.1 with a11 a22 Then for continuous time scale T ζ1− and have μ 0, and by picking m in...
... a linear second order differential equation with retarding argument,” Differentsial’nye Uravneniya, vol 31, pp 622–629, 1995 [7] A L Skubaˇ evski˘, “The oscillatory solutions of a second order linear ... S M Labovski˘, “A condition for the nonvanishing of the Wronskian of a fundamental system of ı solutions of a linear differential equation with retarded argument,” Differentsial’nye Uravneniya, ... solutions satisfying the condition u1 (t)u2 (t) < 0, for t ≥ t0 , (1.4) are established for the system (1.3) In the recent paper by Kiguradze and Partsvania [12] the existence of the Kneser-type...
... Anti-Lyapunov method for systems of discrete equations, Nonlinear Analysis 57 (2004), [9] no 7-8, 1043–1057 [10] D Ya Khusainov and G V Shuklin, Linear autonomous time-delay system with permutation ... investigation goes back to [10] dealing with the linearsystem of differential equations with constant coefficients and constant delay One of the systems considered has the form ˙ x(t) = Bx(t − τ), ... problems for systems of the form (1.3), since the usually used method of steps (being nevertheless hidden in the notion of delayed exponential) gives unwieldy formulas Discrete systems of the...
... and oscillations for systems with sector restricted nonlinearities or linear quadratic stabilization are considered, the associated linear discrete-time periodic Hamiltonian systems have to be ... Hamiltonian systems are a subset of the symplectic systems; if we refer to [26] where systems (1.5) with real coefficients are called canonical, we may say that in the discrete-time case canonical systems ... symplectic systems and Hamiltonian systems (with complex coefficients) are a subset of the J-unitary systems On the contrary, symplectic (or J-unitary) and canonical (or Hamiltonian) systems coincide...
... describes the system The equations derived are limited to linear systems or to systems that can be represented by linear equations over their useful operating range The important concepts of system ... requirements Linear and nonlinear simulations are very helpful in early evaluation of the controlled system, but if the system is to operate in the real word, hardware-in-the-loop and system tests ... allow a linear analysis to be used This textbook considers only linear systems A basic system has the minimum amount of equipment necessary to accomplish the control function After a control system...
... and D Aeyels, Stabilization of positive linear systems Systems and Control Letters 44 (2001) 259–271 16 Ph H A Ngoc and N K Son, Stability radii of linear systems under multiperturbations, Numerical ... Progress in System and Control Theory, Birkh¨user, Basel, 1990, 119-162 a D Hinrichsen and A J Pritchard, On the Robustness of Stable Discrete-Time Linear Systems, In: New Trends in Systems Theory, ... radii of linear discrete-time systems and symplectic pencils, Inter J Nonlinear and Robust Control, (1991) 79–97 11 D Hinrichsen and N K Son, Stability radii of positive discrete-time systems...
... observability conditions of linear autonomous systems’, Nederl Acad Wetensch Proc Ser A, 72, 443–448 15 [11] Hinrichsen, D., Pritchard, A.J (1986), ‘Stability radii of linear systems’, Systems Control Lett., ... problem was considered in [14, 24] for linear delay systems Therefore, it is natural and meaningful to continuous studying controllability radius for linear neutral systems The aim of this paper is ... the controllability radius of linear systems under unstructured perturbations is derived by Esing in [5] After that, formulas for controllability radius of linear systems under structured perturbation...
... Linear Systems x1[n] FIGURE 5-8 Any system with multiple inputs and/or outputs will be linear if it is composed of linear systems and signal additions System A x2[n] x3[n] 97 System B y2[n] System ... for linear systems When two or more linear systems are arranged in a cascade, the order of the systems does not affect the characteristics of the overall combination x[n] System A System B System ... Examples of Linear and Nonlinear Systems Table 5-1 provides examples of common linear and nonlinear systems As you go through the lists, keep in mind the mathematician's view of linearity (homogeneity,...
... Cooperative communication system 1.2 MIMO system 1.3 Single-user AF MIMO relay system 1.4 Multi-user AF MIMO relay system ... generation mobile communication systems and beyond 3 Source Destination Figure 1.2 MIMO system To exploit the benefits of MIMO systems, transceiver design for MIMO systems is of great meaning and ... addressed by linear transceiver design in this thesis Transceiver designs for point-to-point MIMO or multi-user MIMO systems have been widely addressed previously However, for AF MIMO xi relaying system, ...
... can study how linear systems are reduced by instead studying how the associated homogeneous systems are reduced 22 Chapter One Linear Systems Studying the associated homogeneous system has a ... homogeneous linearsystem is a linear surface passing through the origin Finally, we can view the general solution set of any linearsystem as being the solution set of its associated homogeneous system ... in an echelon-form linearsystem are free variables In the echelon form system derived in the above example, x and y are leading variables and z is free 2.3 Example A linearsystem can end with...
... feedback linearization of this non -linear system is presented in [CAL 88] Different techniques are used to transform a non -linear system into a linearsystem The main commonly used approach is to linearize ... non -linear systems Recall that the Hammerstein structure consists of a non -linear static system followed by linear dynamics On the basis of the use of the inverse of the non -linear static system, ... Continuous Linear Systems We can consider linearity as a view of our mind There exists no general technique for the design of controllers for non -linear systems This explains why linear models...
... problem for a linearsystem of differential equations with rational coefficients The goal of this paper is to develop a general theory of “isomonodromy” transformations for linear systems of difference ... Isomonodromy transformations of linear systems of difference equations By Alexei Borodin Abstract We introduce and study “isomonodromy” transformations of the matrix linear difference equation Y (z ... theory for linear matrix differential equations, which is due to Riemann, Schlesinger, Fuchs, and Garnier; see [JMU], [JM] for details Consider a first order matrix system of ordinary linear differential...
... [9] that a system satisfying the above conditions generates languages that are semilinear and can be recognized in polynomial time The definition of linear context-free rewriting systems is deliberately ... a gcfg and its interpretation function m maps symbols onto operations whose yield functions are linear regular operations In order to simplify the remaining discussion we assume that m maps directly ... where the equation is regular (all the variables appearing on one side appear on the other) and linear (the variables appear only once on the left and right) For example, the operations of head...