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Stability and Stabilization of Two‐Dimensional LTI Switched Systems with Potentially Unstable Focus
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Liying Zhu 《Asian journal of control》2015,17(3):892-907
This paper investigates stability and stabilization of two‐dimensional switched linear time‐invariant (LTI) systems with potentially unstable focus. For the case that the origin is a single common focus of all subsystems, we first give continuous positive definite functions related only to the elements of subsystems' state matrices. Then, based on the continuous positive definite functions obtained, this paper proposes several sufficient conditions of stability/asymptotic stability/instability of the kind of switched LTI systems. By means of the stability results proposed, global asymptotic stabilizing controls (GASC), global asymptotic stabilizing switching paths (GASSP) and corresponding algorithms are designed for two‐dimensional switched LTI systems with focus. Finally, two illustrative examples and numerical simulations demonstrate the effectiveness of the new stability and stabilization results obtained in this paper. 相似文献
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极点配置广义稳态Kalman估值器 总被引:1,自引:0,他引:1
应用时域上的现代时间序列分析方法,基于自回归滑动平均(ARMA)新息模型和白噪
声估值器,应用控制理论中的极点配置原理,对线性离散时间广义随机系统提出了极点配置广义
稳态Kalman估值器.它们具有全局渐近稳定性,且通过配置估值器的极点可按指数衰减速率使
初始状态估值的影响快速消失.它们可在统一框架下处理滤波、平滑和预报问题.它们避免了Riccati
方程和最优初始状态估值的计算,因而可减小计算负担.一个仿真例子说明了它们的有效性. 相似文献
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This paper addresses the stability and control problem of the linear positive two‐dimensional (2‐D) continuous‐time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2‐D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state‐feedback controllers is proposed for general delayed 2‐D systems, which ensures the non‐negativity and the stability of the resulting closed‐loop systems. Two examples are given to validate the proposed methods. 相似文献
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This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches. 相似文献
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Bohao Zhu James Lam Xiaoqi Song Hong Lin Jason Ying Kuen Chan Ka-Wai Kwok 《Asian journal of control》2023,25(2):677-694
This paper is concerned with the stability analysis and stabilization of periodic piecewise positive systems. By constructing a time-scheduled copositive Lyapunov function with a time segmentation approach, an equivalent stability condition, determined via linear programming, for periodic piecewise positive systems is established. Based on the asymptotic stability condition, the spectral radius characterization of the state transition matrix is proposed. The relation between the spectral radius of the state transition matrix and the convergent rate of the system is also revealed. An iterative algorithm is developed to stabilize the system by decreasing the spectral radius of the state transition matrix. Finally, numerical examples are given to illustrate the results. 相似文献
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This paper analyses an asymptotic stability of a digitally redesigned control system when the states of the analogue and the digital control systems are approximately matched at every sampling point. The digital redesign is a simple method of converting a given analogue controller to an equivalent digital controller in the sense of state-matching. The concerned state-matching technique is to minimise the norm distance between the discretised closed-loop system matrix of linear analogue control system and that of linear digital control system. It is shown that (i) there exists an upper bound of the norm distance to guarantee the asymptotic stability of the digitally redesigned control system and (ii) the trajectories of the linear analogue and the linear digital control systems coincide at every sampling point if the norm distance is zero. Also, a robustness result is provided in the case that nonlinear perturbations occur in the analogue and the digital control systems. Moreover, design conditions for the developed stability analysis are proposed in terms of linear matrix inequalities. 相似文献