positive forms and stability of linear timedelay systems

... s  ds, 1.8 where P and Q are positive matrices and γ is a positive scalar. Delay independent criteria of stability for some classes of delay neutral systems are developed in 10. The stability of systems ... and P. Yu, Stability of Dynamical Systems, vol. 5 of Monograph Series on Nonlinear Science and Complexity, Elsevier, Amsterdam, the Netherlands, 2007. 12 Ju H. Park and S. Won, “A note on stability ... exponential stability of system 1.1 as well as on estimates of the norms of its solutions and their derivatives in the case of exponential stability and in the case of exponential stability being...

Ngày tải lên: 21/06/2014, 11:20

... Discrete systems of the form (1.1) containing only one delay are often called systems with pure delay. The main goal of the present paper is to extend the notion of the delayed exponential of a matrix ... type technique and retract principle), some of these problems have been investigated, for example, in the recent papers [2–9, 11–13]. REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH ... CONSTANT COEFFICIENTS AND PURE DELAY J. DIBL ´ IK AND D. YA. KHUSAINOV Received 16 January 2006; Accepted 22 January 2006 The purpose of this contribution is to develop a method for construction of solutions of linear...

Ngày tải lên: 22/06/2014, 22:20

... theory of ODE we show that each solution of (3.1) is a solution of a linear equation of the form The Central Exponent and Asymptotic Stability 13 Now we consider again the case of nonlinear ... consisting of a system of ordinary differential equations (ODEs) and a system of algebraic equations so that we can use methods and results of the theory of ODEs. Many results on stability properties of ... exponents of linear DAEs of index 1. In Sec. 3 we investigate exponential asymptotic stability of linear DAEs with respect to small linear as well as nonlinear perturbation. 2. The Central Exponent of...

Ngày tải lên: 06/08/2014, 05:20

... determinist systems: the concept of state 44 2.1.2. Equations of state and equations of measurement for continuous systems 46 2.1.3. Case of linear systems 47 2.1.4. Case of continuous and invariant ... of linear and invariant systems 66 2.4.3. Canonic representation of partially controllable systems 69 2.4.4. Scalar representation of partially controllable systems 73 2.5. Observability of ... of systems 74 2.5.1. General definitions 74 2.5.2. Observability of linear and invariant systems 74 2.5.3. Case of partially observable systems 77 2.5.4. Case of partially controllable and...

Ngày tải lên: 09/08/2014, 06:23

... by equations of state. Asymptotic stability Stability in the broad sense Unstable Figure 1.7. Concepts of stability Another point of view can be adopted where the stability of a system can ... of Linear Systems Figure 1.19. Unit-step response of the second order system ξ ≥ 1 1= ξ : critical state. The roots of the denominator of the transfer function are real and merged, and ... Analysis and Control of Linear Systems In general, the Dirac impulse is a very simplified model of any impulse phenomenon centered in o tt = , with a shorter period than the time range of the systems...

Ngày tải lên: 09/08/2014, 06:23

... 2002. 94 Analysis and Control of Linear Systems NOTE 3.3.– the class of rational systems that can be described by [3.16] or [3.18] is a sub-class of DLTI systems. To be certain of this, let us ... Analysis and Control of Linear Systems Figure 3.5. Bode diagram of the continuous system and its discretization 3.4.5. The problem of sub-sampling Let us consider the case of a “standardized” ... i n is the multiplicity order of i λ and i th the eigenvalue of A. 5 A canonical form called controllable companion. 88 Analysis and Control of Linear Systems Hence, if we suppose...

Ngày tải lên: 09/08/2014, 06:23

... the use of rollouts and in particular the fixed poles and the remaining degrees of freedom, we can mention [MAL 93, MAL 97] and [MAR 94, MAR 99]. 126 Analysis and Control of Linear Systems ... 0): 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of numerous control ... illustrates the invariance properties of the various structures of these canonical forms (indices of controllability, of observability, finite and infinite zeros) and of the associated transformation...

Ngày tải lên: 09/08/2014, 06:23

... of ν 0 . 142 Analysis and Control of Linear Systems A discrete-time deterministic signal y[k],k ∈Zis, by definition, a sequence of complex numbers: y =  y[k]  k∈Z In short, we often speak of ... y 2 )  =  y 1  y 2 [5.9] 152 Analysis and Control of Linear Systems Figure 5.1. Typical power spectrum of an MA (left) or AR (right) model In the case of a single denominator (n c =0), we talk of an AR (autoregressive) model, ... Signals: Deterministic and Statistical Models 153 5.4. Modeling of LTI systems and ARMAX modeling Let us take a linear time-invariant (LTI) system, of impulse response g. The response of this system...

Ngày tải lên: 09/08/2014, 06:23

... the condition of detectability by a careful choice of matrix Q. 162 Analysis and Control of Linear Systems case of multi-control systems. As indicated in Chapter 2, the equations of state can ... at the expense of a stronger control. 176 Analysis and Control of Linear Systems Figure 6.6. Stabilization by quadratic optimization 166 Analysis and Control of Linear Systems Figure ... 174 Analysis and Control of Linear Systems there is a unique matrix P , symmetric and positive semi-defined, solution of the following equation (called discrete...

Ngày tải lên: 09/08/2014, 06:23

... from the point of view of calculation, in terms of linear regression (or linearized), i.e. it leads to a quadratic 196 Analysis and Control of Linear Systems in performing the roles of the procedure, ... K 1  N 10  1+ 1 2 n 1 N 10  [7.21] 222 Analysis and Control of Linear Systems iteration, unstable), interrupt the simulation and the calculation of sensitivity func- tions, hence of the gradient, on a preset upper ... calculation of a criterion whose theoretical value for the current set of parameters diverges (for example, a transfer output error whose poles are, during an 218 Analysis and Control of Linear Systems following...

Ngày tải lên: 09/08/2014, 06:23

... Analysis and Control of Linear Systems Consequently, the field of absolute stability of multi-interval methods (implicit or not depending on the value of 0 ) is the set of à C so that the roots of ... requirements of speed and accuracy accessible in simulation. 8.2. Standard linear equations 8.2.1. Definition of the problem We will adopt the notations usually used to describe the state forms and linear dynamic ... desired and to perform the corre- sponding substitutions. Let us take the example of the classic PID regulator. Let e(t) 230 Analysis and Control of Linear Systems The sizes of blocks 0 and I...

Ngày tải lên: 09/08/2014, 06:23

... study the case of open loop stable systems, that of integrator systems and finally the case of open loop unstable systems. 270 Analysis and Control of Linear Systems We note that when ξ tends ... and the phase is of π − . The image of the ray [0,] `− ∞− is the symmetric curve, with respect to the axis of real numbers. The image of the semicircle of radius ε is an arc of circle of ... other hand. The quality of the feedback control is mainly translated through its stability and the follow-up precision of the output on the input and consequently of the dynamics of this...

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 09/08/2014, 06:23

Ngày tải lên: 07/11/2013, 09:15