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1.
A new algorithm for computations of matrix partial fractions representing the inverse of linear matrix pencil is based on an appropriate expression in matrix form of the Pascal triangle. It concerns singular and nonsingular systems and starts with the inverse of regular matrix linear pencil M(s) = sA0 - A where only A0 is singular, or both A0 and A are singular. Nonsingular systems are considered as a particular case of singular systems. The presented algorithm of the matrix partial fraction expansion is suitable to determine the matrix transfer function, and is computer oriented because all manipulations can be performed on matrices with constant entries only.  相似文献   

2.
This paper is focused on the iterative learning control problem for linear singular impulsive systems. For the purpose of tracking the desired output trajectory, a P-type iterative learning control algorithm is investigated for such system. Based on the fundamental property of singular impulsive systems and the restricted equivalent transformation theory of singular systems, the convergence conditions of the tracking errors for the system are obtained in the sense of λ norm. Finally, the validation of the algorithm is confirmed by a numerical example.  相似文献   

3.
This paper is assigned to study the stability and controllability of fuzzy singular dynamical systems. Some new notions such as granular fuzzy matrix norm, the algebraic operations on the space of fuzzy matrices, fuzzy equilibrium point, and the granular fuzzy transfer function of fuzzy singular dynamical systems are introduced. Furthermore, by presenting some theorems proved in this paper, the fuzzy solutions of fully fuzzy singular dynamical systems are obtained. Moreover, some new notions regarding the analysis of the stability of fuzzy singular dynamical systems are given. The stability analysis underlies the concepts of fuzzy stable, fuzzy critical stable, and fuzzy unstable singular dynamical systems. Besides using the notions of controllability of the fuzzy slow and fast subsystems, the concept of granular controllability of the fuzzy singular dynamical system is investigated.  相似文献   

4.
Most existing consensus control in multi-agent systems (MASs) require agents to update their state synchronously, which means that some agents need to wait for all individuals to complete the iteration before starting the next iteration. To overcome this bottleneck, this paper studied asynchronous consensus problems of second-order MASs (SOMASs) with aperiodic communication. An asynchronous pulse-modulated intermittent control (APIMC) with heterogeneous pulse-modulated function and time-varying control period, which can unify impulsive control and sampled-data control, is proposed for the consensus of SOMASs. A time-varying discrete system is constructed to describe the evolution of the sample values of position and velocity of the SOMAS. Then, by the analysis tools from the stochastic matrix and the properties of the Laplace matrix of graph, some effective conditions are obtained to show the relationship between the convergence of the controlled SOMASs and the control parameters. Finally, a 300-node SOMAS whose topology is a random geographic network is included to verify the feasibility of the proposed control and the correctness of the theoretical analysis.  相似文献   

5.
This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a class of discrete-time singular Markov jump systems with Wiener process and partly unknown transition probabilities. The class of stochastic singular model under consideration is more general and covers the stochastic singular Markov jump time-varying delay systems with completely known and completely unknown transition probabilities as two special cases. Firstly, based on a stochastic Lyapunov–Krasovskii candidate function and an auxiliary vector function, by employing some appropriate free-weighting matrices, the discretized Jensen inequality and combining them with the structural characteristics of the filtering error system, a set of delay-dependent sufficient conditions are established, which ensure that the filtering error system is stochastically admissible. And then, a singular filter is designed such that the filtering error system is not only regular, causal and stochastically stable, but also satisfy a prescribed H∞ performance for all time-varying delays no larger than a given upper bound. Furthermore, the sufficient conditions for the solvability of the H∞ filtering problem are obtained in terms of a new type of Lyapunov–Krasovskii candidate function and a set of linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed method in the paper.  相似文献   

6.
This brief communication establishes a two-step iterative algorithm based on the orthogonal projection for reducing order of the high-order system transfer function or state variable equations. A two-step iterative algorithm which has been developed by the authors (1) consists of the residue and pole (or eigenvalue) optimization with respect to the objective function. Here, the optimum residues in the first step can be determined by using the reciprocal basis in the projection theorem. The reciprocal basis allows one to avoid performing the Grammian inversion. Selecting the new basis, the optimum poles in the second step can be also applied for the orthogonal projection. Although the resulting reduced-order models derived from this geometrical point of view are consistent with models of a two-step iterative algorithm, the algorithm is thus a computationally much simpler way to derive the formula.  相似文献   

7.
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8.
This paper investigates the finite-time control problems for a class of discrete-time nonlinear singular systems via state undecomposed method. Firstly, the finite-time stabilization problem is discussed for the system under state feedback, and a finite-time stabilization controller is obtained. Then, based on which, the finite-time H∞ boundedness problem is studied for the system with exogenous disturbances. Finally, an example of population distribution model is presented to illustrate the validity of the proposed controller. Because there is no any constraint for singular matrix E in the paper, controllers can be designed for more discrete-time nonlinear singular systems.  相似文献   

9.
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10.
An algorithm, amenable for programming on a digital computer, has been presented for the modelling of linear discrete-time systems, as an alternative to the procedure of Shamash (1). The transformations inherent in the procedure are easily accomplished by the synthetic division technique. With the use of modified Cauer form of continued fraction (MCF), the new method matches a set of both the time-moments and Markov parameters of the system and of the model, as in the procedure of Parthasarathy and Singh (2), giving a better approximation to the system response at all times. A distinct feature of the proposed algorithm compared with the earlier methods of discrete system reduction (1),(2), is that a number of reduced-order models are generated simultaneously; this allows scope for better selection in choosing the right model for system analysis and design.  相似文献   

11.
This paper is to study the mean square stabilizability and regional stability of discrete-time mean-field stochastic systems. Firstly, a necessary and sufficient condition is presented via the spectrum of linear operator to illustrate the stabilizability of discrete-time mean-field stochastic systems. B(0, γ)-stabilizability is introduced and transformed into solving linear matrix inequalities (LMIs). Secondly, BM-stability is characterized, especially, the stabilities of circular region, sector region and annulus regions are discussed extensively. Finally, as applications, it is shown that B(0, γ1; γ2)-stability has close relationship with the decay rate of the system state response and the Lyapunov exponent.  相似文献   

12.
Given the linear system x = Ax - bu, y = cTx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by uopt(x) = h(cTx), where the function h(y) must satisfy the conditions ky2?h(y)y>0 for y≠0, h(0) = 0 and existence of h-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function.  相似文献   

13.
Based on the Chebyshev series, a directly computational formulation in matrix form is established for evaluating the optimal control and trajectory of time-delay systems. In a comparison with the previous work (3, Int. J. Control, Vol. 41, pp. 1221-1234, 1985), the formulation is shown to be more straightforward and convenient for digital computation. Thus the difficulty in obtaining a solution of the two-point boundary-value problem with both delayed and advanced arguments is circumvented. An example compares the actual solution with the one obtained using the technique of this paper.  相似文献   

14.
This paper is concerned with the observer-based H∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.  相似文献   

15.
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16.
A two-step iterative method (1,2) for a reduction in the order of linear continuous-time systems, given in the state equation or the transfer function, is extended to reduce discrete-time systems. The method requires the optimization of the residues and eigenvalues (or poles) belonging to an objective function. The objective function to be minimized is chosen as the finite sum of the squares of the error between the step responses of the reduced model and the original system. This scheme is continued cyclically until the objective function is satisfactorily minimized. By investigating the initial selection of the eigenvalues in the reduced-order model, it is found that the dominant eigenvalues of the original system give a good approximation. Further, the resulting model is always stable, assuming the original system is stable. As shown in a numerical example, the proposed method is superior to the other methods of model reduction in both steady-state and transient responses, and in the value of the sum of the squares of the error.  相似文献   

17.
This paper investigates the problem of mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay. The considered systems are with mode-dependent singular matrices Er(k)Er(k). By using the free-weighting matrix method and the Lyapunov functional method, delay-dependent sufficient conditions which guarantee the considered systems to be mean-square exponentially stable are presented. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed methods.  相似文献   

18.
This paper is devoted to the characterization of L∞-gain for positive singular systems with time-varying delays. First, we introduce an augmented system to replace the original system in order to analyze the positivity of singular systems with time-varying delays. By investigating the monotonicity of state trajectory, the L∞-gain for singular system with constant delays is characterized. Then, by comparing the trajectories of time-varying delay system and constant delay case, we finally propose the L∞-gain for singular system with time-varying delays. It is shown that the L∞-gain of positive singular systems is independent of the magnitude of delays.  相似文献   

19.
This paper investigates the finite-time stability (FTS) and finite-time stabilization for a class of nonlinear singular time-delay Hamiltonian systems, and proposes a number of new results on these issues. Firstly, an equivalent form is obtained for the nonlinear singular time-delay Hamiltonian systems by the singular matrix decomposition method, based on which some delay-independent and delay-dependent conditions on the FTS are derived for the systems by constructing a kind of novel Lyapunov function. Secondly, we use the equivalent form as well as the energy shaping plus damping injection technique to investigate the finite-time stabilization problem for a class of nonlinear singular port-controlled Hamiltonian (PCH) systems with time delay, and present a specific control design procedure for the systems. Finally, we give several illustrative examples to show the effectiveness of the results obtained in this paper.  相似文献   

20.
Sarmanov introduces the idea of maximal correlation function and applies it to his investigation of stationary Markov processes (1,2,3). We demonstrate some additional properties of the maximal correlation function as a measure of the dependence structure of stationary processes and present some applications of the maximal correlation function in generalizing applications of the usual correlation function to, for example, equivalent rectangular bandwidth and quadratic mean ergodicity.  相似文献   

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