Simultaneous stabilization of MIMO systems with integral action controllers

Simultaneous stabilization with asymptotic tracking of step-input references is explored for linear, time-invariant, multi-input multi-output stable plants. Necessary conditions are presented for existence of simultaneous integral-action controllers and existence of simultaneous PID-controllers. A systematic simultaneous PID-controller synthesis method is proposed under a sufficient condition.     

Strong stabilization of MIMO systems via unimodular interpolation in H

In this paper, the strong stabilization problem of multivariable linear timeinvariant systems is considered. The problem is categorized into minimum and non-minimum phase systems. When the given system is minimum phase, the solution requires a stable inverse of a particular stable transfer function matrix; while for a non-minimum phase system, the solution requires an inner-outer factorization, whose outer part is unimodular in RH, and an interpolation in RH. The formulation of the two cases will be modified so that the conditions for the existence of stable inverse or unimodularity of the outer part are satisfied. When the system is strictly proper it is shown that the problem is more technically involved.     

Output feedback stabilization of MIMO non-linear systems via dynamic sliding mode

Previous work on asymptotic stabilization of MIMO non-linear systems using dynamic sliding mode control to produce dynamic state feedback has been generalized to dynamic output feedback. All the states in the feedback controller are replaced with estimated states which come from a semi-high-gain observer. The bound on the observer gain is explicitly given, which depends on some previously chosen design parameters. If the given differential input–output (I–O) system is minimum phase and proper, local uniform asymptotic output feedback stabilization can be achieved. In addition, the restriction on the stability of the zero dynamics has been relaxed to weakly minimum phase and semi-global results are obtained under some mild conditions. The stability of the closed-loop system is based on some stability results of triangular systems when continuous or discontinuous controllers are adopted. Two pertinent examples are given to illustrate the design method. Copyright © 1999 John Wiley & Sons, Ltd.     

线性系统的同时镇定问题

线性系统的同时镇定问题,是系统与控制理论中的基本问题,有着广泛的理论意义和应用价值.本文介绍了线性系统同时镇定问题的研究现状和最新进展.首先回顾了同时镇定问题的研究内容、基本方法及相关结果.其次,从理论求解和控制器设计的角度对线性系统同时镇定研究中著名的"香槟问题","比利时巧克力问题"和"威士忌问题"进行了分析探讨,并基于不等式型定理机器证明理论,给出了线性系统同时镇定问题的相关工作.最后指出了对于同时镇定多个线性系统方面的若干研究方向.     

Simultaneous stabilization of nonlinear systems

We study the problem of simultaneous stabilization of a given set of nonlinear plants by one nonlinear, not necessarily stable compensator. We obtain a necessary and sufficient condition under which there is a single compensator which stabilizes a given set ofnnonlinear plants. This note emphasizes the importance of the following problem: when is a nonlinear unstable plant stabilizable by an incrementally stable compensator.     

Simultaneous stabilization via linear state feedback control

The problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered. The authors assume that the complete state can be measured and seek a (static) linear state feedback control law. Sufficient conditions for such full state gains to exist are given and they show via several examples how stabilizing compensators can be designed     

Simultaneous stabilization of single-input single-output discretetime systems

The problem of finding one compensator which simultaneously stabilizes a family of single-input-single-output (SISO) discrete-time plants is considered. The family of plants is described by the transfer functions {Pz, q): q∈Q}, which are generated via a z-transformation. A number of assumptions describing the set of allowable plants are then given. These assumptions include some regularity conditions on the plants and a minimum-phase requirement. The satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator C(z) for simultaneous stabilization. An iterative computation method is provided for control design     

Simultaneous stabilization via static output feedback and statefeedback

In this paper, the simultaneous stabilization problem is considered using the matrix inequality approach. Some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi-input/multi-output (MIMO) plants via static output feedback and state feedback are obtained in the form of coupled algebraic Riccati inequalities. It is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term. A heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities. The effectiveness of the approach is illustrated by numerical examples     

Global stabilization of MIMO minimum-phase nonlinear systems without strict triangular conditions

An extension of backstepping to a class of multivariable minimum-phase nonlinear systems is proposed. The systems are assumed to be in a special interlaced form which includes a lower triangular form as a special case. The extension involves the recursive application of backstepping and augmentation.     

Simultaneous stabilization for a collection of single-input nonlinear systems

This paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single-input nonlinear systems. The control Lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time-invariant simultaneously stabilizing state feedback controllers. Additionally, a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented. For any collection of second-order (and third-order) feedback linearizable systems in canonical form, global simultaneous stabilization via a single state feedback controller is shown to be always possible. Two examples are included for illustration.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

Adaptive stabilization of linear systems via switching control

In this paper, we develop a method for adaptive stabilization without a minimum-phase assumption and without knowledge of the sign of the high-frequency gain. In contrast to recent work by Martensson [8], we include a compactness requirement on the set of possible plants and assume that an upper bound on the order of the plant is known. Under these additional hypotheses, we generate a piecewise linear time-invariant switching control law which leads to a guarantee of Lyapunov stability and an exponential rate of convergence for the state. One of the main objectives in this paper is to eliminate the possibility of "large state deviations" associated with a search Over the space of gain matrices which is required in [8].     

Robust stabilization of chained systems via hybrid control

The problem of global robust exponential stabilization of nonholonomic chained systems is addressed and solved by means of a hybrid state feedback control law. It is shown that the control law yields global exponential stability and global robustness against a class of small measurement errors, actuator noises and exogenous disturbances.     

Optimal stabilization of linear systems via decentralized outputfeedback

Presents an approach to the optimal stabilization of a linear time-invariant system via decentralized control. The class of controllers considered does not restrict the controller to be finite dimensional or time invariant. In fact, the controller structure proposed can be regarded as a form of time varying sampled data control. The main result of the paper presents a scheme for constructing a collection of decentralized controllers which stabilizes the system and is optimal with respect to a quadratic performance index     

Finite-time stabilization of linear systems via impulsive control

This paper introduces a new concept of finite-time stability of linear time-invariant impulsive systems. The sufficient condition of finite-time stability of the system via impulsive control at fixed times and variable times is obtained, respectively. Such sufficient conditions of finite-time stabilization are given in terms of matrix inequalities. A numerical example is presented to illustrate the efficiency of the proposed results.     

Robust stabilization of LTI systems via indirect adaptivecontrollers

This paper presents a robust indirect adaptive stabilization controller for systems with linear time-invariant (LTI) nominal parts, uncertain dynamic errors, and bounded disturbances. The a priori knowledge required for designing the adaptive controller is that the nominal part of the system is of known order and is stabilizable     

Output feedback stabilization of nonlinear MIMO systems having uncertain high-frequency gain matrix

The purpose of this paper is to provide a method for (semi-global) asymptotic stabilization of a nonlinear minimum-phase MIMO system, under a mild hypothesis of the so-called “high-frequency gain” matrix. This result is based on a non-trivial extension, to the MIMO setting, of the approach based on the use of extended observers. As a byproduct, a dynamic output feedback control is obtained, that asymptotically stabilizes the equilibrium of the closed-loop system, in spite of uncertainties in the high-frequency gain matrix.     

Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems

This paper investigates simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian (PCH) systems and proposes a number of results on the design of simultaneous stabilization controllers for the PCH systems. Firstly, the case of two PCH systems is studied. Using the dissipative Hamiltonian structural properties, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. For the case that there exist parametric uncertainties in the two systems’ Hamiltonian structures, an adaptive simultaneous stabilization controller is proposed. When there are external disturbances and parametric uncertainties in the two systems, two simultaneous stabilization controllers are designed for the systems: one is a robust controller and the other is a robust adaptive one. Secondly, the case of more than two PCH systems is investigated, and a new result is proposed for the simultaneous stabilization of the systems. Finally, two illustrative examples are studied by using the results proposed in this paper. Simulations show that the simultaneous stabilization controllers obtained in this paper work very well.