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1.
This note is concerned with the problem of stabilizing an uncertain linear system via state feedback control. An uncertain system which admits a stabilizing state feedback control and some associated quadratic Lyapunov function is said to be quadratically stabilizable. In a number of recent papers, conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control. These papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result. This note presents an example which shows that this implication is not true for more general uncertain linear systems. To this end, we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control. 相似文献
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This paper investigates the stabilizability of uncertain linear time-invariant (LTI) systems via structurally constrained controllers. First, an LTI uncertain system is considered whose state-space matrices depend polynomially on the uncertainty vector, defined over some region. It is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region, then it is stabilizable by a controller with the same structure in all points belonging to the region, except for those located on an algebraic variety. Thus, if a system is stabilizable via a constrained controller at the nominal point, then it is almost always stabilizable at any operating point around the nominal model. It is also shown how this algebraic variety (or the dominant subvariety of it) can be computed efficiently. The results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the LTI systems, in addition to new ones. 相似文献
3.
This paper considers the problems of robust stability analysis and robust stabilization for uncertain singular systems with norm-bounded time-varying uncertainties. The robust stability problem is solved via the notion of generalized quadratic stability which guarantees that the uncertain singular system is stable, regular and impulse free simultaneously for all admissible uncertainties, while the robust stabilization problem is solved via the notion of generalized quadratic stabilizability. An algebraic approach is adopted in the paper. Our main results are extensions of some existing results on uncertain regular systems for singular systems. 相似文献
4.
Quadratic Stabilizability for Polytopic Uncertain Switched Linear Systems via Switched Observer
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In this paper, we study a quadratic stabilizability problem via switched observer for uncertain continuous‐time switched linear systems in the sense that the subsystem's matrices are represented as a polytopic linear combination of vertex matrices. Firstly, sufficient conditions for polytopic uncertain continuous‐time switched linear systems to be quadratically stabilizable via state feedback are summarized. Next, sufficient conditions for polytopic uncertain switched linear systems to be quadratically stabilizable via switched observer are given under the assumption that output matrices of subsystems have no uncertainties. Further, a numerical example is also investigated. 相似文献
5.
A stabilizing linear static controller is discovered for a linear time-varying uncertain system of Petersen. We use the concept of a sandwich cone decomposition to show that Petersen's system is stabilizable by linear static controllers. We establish the surprising result that Petersen's system is stabilizable against time-varying uncertainties on any given compact subset of the uncertainty controllability space. Our work suggests the use of “scalar-quadratic” Lyapunov functions, a special subclass of polyhedral Lyapunov functions, in establishing stability for other linear time-varying uncertain systems, and it reopens the study of the conjecture: stabilizability via nonlinear control always implies stabilizability via linear control 相似文献
6.
A stabilization algorithm for a class of uncertain linear systems 总被引:16,自引:0,他引:16
This paper presents an algorithm for the stabilization of a class of uncertain linear systems. The uncertain systems under consideration are described by state equations which depend on time-varying unknown-but-bounded uncertain parameters. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Furthermore, the solution to this Riccati equation defines a quadratic Lyapunov function which is used to establish the stability of the closed-loop system. This leads to a notion of ‘quadratic stabilizability’. It is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable.The paper also deals with a notion of ‘overbounding’ for uncertain linear systems. This procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems. Also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process. 相似文献
7.
本文研究了不确定线性时滞系统的稳定化鲁棒控制器设计问题,给出了一类不确定线性时滞系统稳定化鲁棒控制器的设计方法,对于一般的不确定线性时滞系统,如果它们的标称系统是二次型能稳的,则该不确定线性时滞系统也是能稳的,且给出了其稳定化控制器的设计方法。 相似文献
8.
This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown. 相似文献
9.
In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix. 相似文献
10.
《Automatic Control, IEEE Transactions on》1994,39(1):22-32
This paper investigates the stabilization problem of linear uncertain systems via constant state feedback control. The systems under consideration contain time-invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems. The criterion for the asymptotic stability of the closed-loop system, obtained when a state feedback control is applied, is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane. First, the author shows that to insure an interval system stabilizable, some entries of the system matrices must be sign invariant. More precisely, the number of the least-required, sign-invariant entries in system matrices is equal to the system order. Then, the author studies the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign-invariant entries in proper locations. After dividing all standard systems into some subsets by the uncertainty locations, the author then derives necessary and sufficient conditions under which every system in a subset is stabilizable, regardless of its parameter varying bounds. The conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a “generalized antisymmetric stepwise configuration”. For an interval system satisfying the stabilizability conditions, a computational control design procedure is also provided and illustrated via an example. The result is further generalized for nonstandard systems via linear transformation 相似文献
11.
《Fuzzy Systems, IEEE Transactions on》2009,17(3):518-531
12.
广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法 总被引:6,自引:1,他引:5
考虑广义不确定系统的鲁棒稳定性及鲁棒镇定问题.提出了广义不确定系统'广义二次稳定'及'广义二次可镇定'的概念,利用矩阵不等式,分别得到了所考虑广义不确定系统广义二次稳定及广义二次可镇定的充要条件,而且,使广义不确定系统鲁棒镇定的状态反馈控制律的设计可通过求解一给定的矩阵不等式而得到. 相似文献
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研究多通道不确定时滞大系统的鲁棒分散H∞控制问题. 假定不确定性是时不变、范数有界, 且存在于系统、时滞和输出矩阵中. 主要针对动态输出反馈控制问题. 基于Lyapunov稳定性理论, 通过设定Lyapunov矩阵为合适的块对角结构, 采用矩阵替换的方法推导出了使多通道不确定时滞大系统可鲁棒镇定, 且满足一定的扰动水平的时滞依赖充分条件即线性矩阵不等式(LMI) 有可行解, 并且给出了具有期望阶数的分散鲁棒控制器的设计方法. 数值例子说明了本文提出方法的有效性. 相似文献
15.
This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. 相似文献
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This paper shows that the matrix inequality conditions for stability/stabilizability of linear differential inclusions derived from two classes of composite quadratic functions are not conservative. It is established that the existing stability/stabilizability conditions by means of polyhedral functions and based on matrix equalities are equivalent to the matrix inequality conditions. This implies that the composite quadratic functions are universal for robust, possibly constrained, stabilization problems of linear differential inclusions. In particular, a linear differential inclusion is stable (stabilizable with/without constraints) iff it admits a Lyapunov (control Lyapunov) function in these classes. Examples demonstrate that the polyhedral functions can be much more complex than the composite quadratic functions, to confirm the stability/stabilizability of the same system. 相似文献
18.
This paper considers the problem of optimal guaranteed cost control of an uncertain system via output feedback. The uncertain system under consideration contains an uncertainty block subject to an integral quadratic constraint. The cost function considered is a quadratic cost function defined over an infinite time interval. The main result of the paper gives a necessary and sufficient condition for the existence of a guaranteed cost controller guaranteeing a specified level of performance. This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation. The resulting guaranteed cost controller is in general time-varying. © 1997 by John Wiley & Sons, Ltd. 相似文献
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This paper investigates the problem of designing a state feedback control to stabilize an uncertain nonlinear system. We focus attention on the amplitude (norm) of the controller which is used to achieve this end. The uncertain system is described by a state equation which contains uncertain parameters which are unknown but bounded. A Lyapunov function is used to establish the stability of the closed loop system. The paper gives necessary and sufficient concitions for the uncertain system to be stabilizable with a given Lyapunov function. Furthermore, a procedure is indicated for the construction of the desired feedback control law. 相似文献