A Lyapunov equation for 2 D singular general discrete state space model is introduced, The relationship between asymptotic stability, the roots of the characteristic polynomial and the 2 D matrix Lyapunov equation is studied. Sufficient conditions for asymptotic stability of the system are presented.

引入 2 - D奇异一般离散状态空间模型的 L yapunov方程 ,探讨了该模型的渐近稳定性、特征多项式的根以及 2 - D L yapunov矩阵方程间的关系 ,给出了系统渐近稳定性的充分条件。

This article tells us how to structure a Markov chain with the strong Markov property in a general discrete state space E,to use the " resolvent property " and to take the " Ray-Knight compactification " of the state space E as a bridge.

It avoids the matrix inverse operation. Meanwhile, the solutions of discrete time state equations and the pulse transfer function can also be obtained easily.

The location observer defined the current location of the hybrid system by Finite State Machine (FSM), while the discrete time state observer estimated the evolution of the discrete time state of the hybrid system by Luenberger observers.

Greedy and periodic control strategies based on the description of hybrid automata are discussed to control the switch sequence of discrete states from the perspective of system safety by analyzing characteristics of the typical hybrid system, three-tank flow system.

The control inputs effect on system states (mainly effect on discrete states) are (analyzed.) The switching of discrete states may help to improve the observability of some linear hybrid system which is unobservable before discrete switch.

The paper presents an adaptive dynamic matrix control algorithm based on the Laguerre model of the unit step response of a plant. The discrete - time state space form of the Laguerre model and the Laguerre network for calculating Laguerre model coefficients are given.

This LDP holds for any discrete state space Markov chain, not necessarily ergodic or irreducible.

It is shown that the effect of a local field may result in a shift, narrowing, or broadening of the resonance, as well as in a change in its amplitude and the character of interference of the discrete state with the continuum.

The cross sections in the region of the overlapping autoionizing Rydberg states 5p5(2P1/2)6d' J = 1 and 5p5(2P1/2)8s' J = 1 resonantly coupled with the discrete state 5p5(2P3/2)7p[1/2]1 in the xenon atom are calculated.

The main attention is given to the behavior of the 1s electron ionization cross section near and above the threshold with simultaneous excitation of the outer 2s electron to a discrete state.

We obtain the conditions for complete population transfer through an autoionizing state in terms of asymmetry parametersq, which characterize the coupling strength between a discrete state and a continuum.

Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta Ji and Jf.

The interaction of atoms with a phonon field causes spontaneous transitions between the discrete states of the trap.

It is shown that a substantial contribution to χ(3) is made by a large number of discrete states into which the valence and conduction bands are split in the presence of three-dimensional confinement.

A test for identity is worked out by comparing the discrete states of the echo signal from an object to be identified and the states typical of the echo signal from a known object.

The explicit analytical expressions of transition form factors from arbitrary discrete states to continuum are obtained in terms of classical polynomials.

An H∞ Output Feedback Control for Discrete-Time State-Delayed Systems

The time-course behavior of these cell kinetic parameters was predicted by solving the discrete-time state equations which characterize the dynamics of tumor-drug interactions.

For both subsystems a discrete-time state-space model was derived using the Control Toolbox of Matlab.

In this paper, we are interested in finding a solution to the discrete-time state feedback H2 synthesis problem.

The model of subnetwork i is a linearized discrete-time state-space model.

Theory on the two dimensional state space has been further developed as a model appropriate to Kalman's filtering for image processing since R.P. Roesser established it in 1975. As a review, this paper lays stress on introducing the recent research works on the Roesser's discrete state space model of two dimensions which includes such concepts from one to two dimensions as the general response formula, the state-transitiom matrix, the 2-D Cayley-Hamilton theorem and the observability and controllability. The...

Theory on the two dimensional state space has been further developed as a model appropriate to Kalman's filtering for image processing since R.P. Roesser established it in 1975. As a review, this paper lays stress on introducing the recent research works on the Roesser's discrete state space model of two dimensions which includes such concepts from one to two dimensions as the general response formula, the state-transitiom matrix, the 2-D Cayley-Hamilton theorem and the observability and controllability. The author gives proof of a response function theorem (cf. section 5, eq. (4.6)) by means of frequency domain other than the proof by Roesser[3]who utilized the time domain. Also, the author gives proof of the observability and controllability in the two dimensional system which are unproved in [3] and [4] in bibliography. Several examples are given, one is cited in illustration of the concept of Cayley-Hamilton theorem and three are cited to demonstrate the realization of the 2-D recursive filters. The practical task to be Developed in near future is mainly to continue the application of Roesser's discrete state space model to Kalman's filtering for image processing. However, some theorems concerned were proved so tediously and so complicated in operation that to simplify and improve them would be of necessity.

This paper attempts to apply Walsh transforms to the state-space analysis of linear discrete-time systems. A cyclic shift-theorem of Wal'sh transforms presented by Cheng and Liu is first extended, and with the aid of Walsh transforms of the discrete state equations, a simple numerical formula for solving the state equations in the sequence domain is derived, from which a group of cyclic solutions of zero-state,response of a system can be obtained. An illustrative example is given.

The digital simulation method on basis of e~(AT) presented in this paperconsists in treating oarious continuous, linear, constant parts of the systemsimulated as subsystems which are desoribed by systems of discrete stateequations. Then, these subsystems and various non-linear or time-varyingparts are interconnected and thus digital simulation of the whole system isimplemented. This method of simulation possesses the merits of fast comp-uting rate, high accuracy and versatilety. The main point described in this...

The digital simulation method on basis of e~(AT) presented in this paperconsists in treating oarious continuous, linear, constant parts of the systemsimulated as subsystems which are desoribed by systems of discrete stateequations. Then, these subsystems and various non-linear or time-varyingparts are interconnected and thus digital simulation of the whole system isimplemented. This method of simulation possesses the merits of fast comp-uting rate, high accuracy and versatilety. The main point described in this paper is concerning the computationof the coefficient matrixes of the subsystems using analytir method whichhas the merit in the amount of computation and accuracy of simulationindependent of the step size chosen with the (somewhat laboursome) program.