共查询到20条相似文献,搜索用时 205 毫秒
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广义系统具有正定解的Lyapunov方程 总被引:1,自引:0,他引:1
本文研究线性广义系统有正定解的Lyapunov方程,给出广义系统稳定等价于Lyapunov方程有正定解,进一步研究了广义系统R-能观,稳定和Lyapunov方程存在正定解三者之间的关系。基于该Lyapunov方程,给出广义系统允许(正则,稳定,无脉冲)的等价条件。 相似文献
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针对一类状态变量中含有时滞的线性系统,提出了函数观测器设计的一种参数方法。给出了函数观测器存在的充要条件。基于Lyapunov稳定理论和广义Sylvester矩阵方程的完全参数化解,给出了时滞系统函数观测器设计算法。两个数值例子说明了提出算法的简单性、有效性。该方法提供了进一步满足其他性能要求的设计自由度。 相似文献
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广义线性系统的干扰解耦观测器设计 总被引:6,自引:0,他引:6
提出了广义线性系统的Luenberger函数观测器关于干扰解耦的充要条件,并进一步基于广义Sylvester矩阵方程的显式通解给出了干扰解耦观测器的参数化设计方法.这种方法首先给出了观测器增益矩阵的参数表示,然后通过结合观测器增益矩阵的参数表示和提出的干扰解耦条件,给出了设计广义线性系统干扰解耦观测器的算法.数值例子说明了本文设计方法的有效性. 相似文献
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This paper presents an algorithm for the construction of a solution of the generalized Lyapunov equation. It is proved that the polynomial matrix factorization relative to the imaginary axis may be reduced to the successive solution of Lyapunov equations, i.e. the factorization is reduced to the solution of a sequence of generalized Lyapunov equations, not to the solution of generalized Riccati equation. 相似文献
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Simultaneous eigenvalue bounds for the solution of the unified non-stationary Lyapunov matrix equation are presented. When the solution becomes stationary, the results reduce to bounds of the unified type algebraic Lyapunov equation. In the limiting cases, the results reduce to bounds for the solution of the differential and difference Lyapunov equations. The bounds given in this paper are a generalization of some existing bounds obtained separately for the continuous and discrete type stationary and non-stationary Lyapunov equations. 相似文献
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具有对称循环结构的大系统Riccati方程的求解 总被引:3,自引:1,他引:3
本文研究了具有对称循环结构的大系统的代数Riccati方程和Lyapunov矩阵方程的求解问题,结果表明,这类系统的代数Riccati方程和Lypapunov矩阵方程的求解问题可以简化为求解N/2+1个独立的低阶方程,做为一个应用,这类系统的二次型最优控制问题和鲁棒二次型最优控制问题也可以简化。 相似文献
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In this paper we construct a sequence of Lyapunov algebraic equations,whose solutions converge to the solutions of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems. The obtained solutions are positive semidefinite, stabilizing, and unique. The proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced-order decoupled Lyapunov equations, Several examples are included to demonstrate the procedure 相似文献
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In this paper, a method for the parallel solution of large sparse matrix equations is presented. The method is based on the balanced bordered block diagonal (BBD) decomposition which is applied in conjunction with the successive over-relaxation (SOR) iterative method to solve large Lyapunov equations in the Kronecker sum representation. A variety of experimental results will be presented, including solutions of Lyapunov equations with matrices as large as 1993×1993 相似文献
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In recent years, several bounds have been reported for the solution of the continuous and the discrete Lyapunov equations. Using the unified Lyapunov equation, we give in this paper bounds for the solution of this equation. In the limiting cases, the bounds reduce to existing bounds for both the continuous and discrete Lyapunov equations. 相似文献
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JÜRGEN GARLOFF 《International journal of control》2013,86(2):423-431
We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation. 相似文献
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Stefano Battilotti 《Asian journal of control》2012,14(4):924-935
In this paper a generalized class of filtered Lyapunov functions is introduced, which are Lyapunov functions with time‐varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability properties as Lyapunov functions. Tools are given for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally stabilizing dynamic feedback laws for block‐feedforward systems with stabilizable linear approximation. 相似文献
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PHILIP S. M. CHIN 《International journal of control》2013,86(4):1561-1567
A new method, called the intrinsic method, is proposed in this paper to derive suitable Lyapunov functions for a general class of non-linear systems expressed in state variables as n first-order non-linear differential equations. This method, which applies the integration-by-parts procedure, derives a Lyapunov function directly from the differential equations under study. 相似文献