Stabilization of persistently excited linear systems by delayed feedback laws

This paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback is indeed possible, generalizing a previous result already known for non-delayed feedback laws.     

Stabilization of nonlinear systems: A bilinear approach

This paper gives a necessary and sufficient condition for the stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.     

Stabilization of nonholonomic chained systems via nonregular feedback linearization

This paper addresses the problem of feedback stabilization of nonholonomic chained systems within the framework of nonregular feedback linearization. Firstly, the nonsmooth version of nonregular feedback linearization is formulated, and a criterion for nonregular feedback linearization is provided. Then, it is proved that the chained form is linearizable via nonregular feedback control, thus enable us to design feedback control laws using standard techniques for linear systems. The obtained discontinuous control laws guarantee convergence of the closed-loop system with exponential rates. Finally, simulation results are presented to show the effectiveness of the approach.     

Some remarks on stabilization by means of discontinuous feedbacks

By means of Ryan's necessary condition and of some examples, we see how the interpretation of solutions of systems with discontinuous right-hand side influences stabilizability results for systems which do not admit continuous stabilizing feedback laws.     

Stabilization of continuous-time switched nonlinear systems

The paper considers three problems for continuous-time nonlinear switched systems. The first result of this paper is a open-loop stabilization strategy based on dwell time computation. The second considers a state switching strategy for global stabilization. The strategy is of closed loop nature (trajectory dependent) and is designed from the solution of what we call nonlinear Lyapunov–Metzler inequalities from which the stability condition is expressed. Finally, results on the stabilization of nonlinear time varying polytopic systems are provided.     

Continuous stabilization controllers for singular bilinear systems: The state feedback case

Global asymptotic stabilization for a class of singular bilinear systems is first studied in this paper. New approaches are developed by means of the LaSalle invariant principle for nonlinear systems. A new set of sufficient condition is first derived via the continuous static state feedback, the feedback not only guarantees the existence of solution but also the global asymptotical stabilization for the closed loop system.     

On the stabilization of switched linear stochastic systems with unobservable switching laws

This paper is concerned with the stabilization problem of switched linear stochastic systems with unob- servable switching laws. In this paper the system switches among a finite family of linear stochastic systems. Since there are noise perturbations, the switching laws can not be identified in any finite time horizon. We prove that if each individual subsystem is controllable and the switching duration uniformly has a strict positive lower bound, then the system can be stabilized by using a controller that uses online state estimation.     

On the stabilization of switched linear stochastic systems with unobservable switching laws

1 Introduction Consider the following switched linear stochastic system dx(t) = Aθtx(t)dt +Bθtu(t)dt + Fθtdwt, E x0 2 < ∞ (1) where x0 = x(0). The system state x(t) ∈ Rn is completely observable and u(t) ∈ Rr is the input. The system noise {wt} is an l-dimensional standard Wiener process, which is independent of {x(s),s t}. Aθt, Bθt, Fθt are coefficient matrices with suitable dimensions. The switching law (or signal) θt : [0, ∞) → Θ is a piecewise constant function of time. I…     

Stabilization and optimization of switched linear systems

In this paper, we establish the equivalence among switched convergency, asymptotic stabilizability, and exponential stabilizability for force-free switched linear systems, and discuss the implication to the infinite-time horizon optimal switching problem. We show that, for a general cost function under mild assumptions, the finiteness of the optimal cost is equivalent to the asymptotic stabilizability of the switched linear system. Finally, we prove the equality between the optimal costs for the switched system and for the relaxed differential inclusion.     

Overcoming the limitations of adaptive control by means of logic-based switching

In this paper we describe a framework for deterministic adaptive control which involves logic-based switching among a family of candidate controllers. We compare it with more conventional adaptive control techniques that rely on continuous tuning, emphasizing how switching and logic can be used to overcome some of the limitations of traditional adaptive control. The issues are discussed in a tutorial, non-technical manner and illustrated with specific examples.     

Stabilizing switching design for switched linear systems: A state-feedback path-wise switching approach

This paper addresses the problem of switching stabilization for discrete-time switched linear systems. Based on the abstraction-aggregation methodology, we propose a state-feedback path-wise switching law, which is a state-feedback concatenation from a finite set of switching paths each defined over a finite time interval. We prove that the set of state-feedback path-wise switching laws is universal in the sense that any stabilizable switched linear system admits a stabilizing switching law in this set. We further develop a computational procedure to calculate a stabilizing switching law in the set.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems con- cerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization prob- lem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Stabilization for state/input delay systems via static and integral output feedback

This paper addresses the static and integral output feedback stabilization problems of continuous-time linear systems with an unknown state/input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback stabilizability are proposed in terms of nonlinear matrix inequalities with a free parameter matrix introduced. These new characterizations possess a special structure, which leads to linearized iterative computation. The effectiveness and merits of the proposed approach are shown through numerical examples.     

离散时滞切换系统的无记忆状态反馈镇定

针对一类子系统为离散时滞系统的切换系统,研究了稳定性与无记忆状态反馈镇定问题．采用多李雅普诺夫函数法,首先以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统渐进稳定的一个充分性条件;然后给出了系统无记忆状态反馈镇定的控制器设计方案,并将结果推广到不确定离散时滞切换系统;最后用仿真算例验证了所提出设计方案的可行性。     

Stabilisability of nonlinear systems by means of time-dependent switching rules

Given a family of linear systems which admit an asymptotically stable convex combination, the existence of stabilising time-dependent switching rules can be proved by using the Baker–Campbell–Hausdorff formula for exponentials. The control laws obtained in this way are periodic, fast switching and independent of the initial state. We prove that under a similar assumption, the approach can be extended to provide stabilising time-dependent switching rules for the families of nonlinear vector fields, as well. However, the resulting control law, in general, is not periodic, not fast switching and it may depend on the initial state.     

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.     

Stabilization of exponentially unstable discrete-time linear systems by truncated predictor feedback

Predictor state feedback solves the problem of stabilizing a discrete-time linear system with input delay by predicting the future state with the solution of the state equation and thus rendering the closed-loop system free of delay. The solution of the state equation contains a term that is the convolution of the past control input with the state transition matrix. Thus, the implementation of the resulting predictor state feedback law involves iterative calculation of the control signal. A truncated predictor feedback law results when the convolution term in the state prediction is discarded. When the feedback gain is constructed from the solution of a certain parameterized Lyapunov equation, the truncated predictor feedback law has been shown to achieve asymptotic stabilization of a system that is not exponentially unstable in the presence of an arbitrarily large delay by tuning the value of the parameter small enough. In this paper, we extend this result to exponentially unstable systems. Stability analysis leads to a bound on the delay and a range of the values of the parameter for which the closed-loop system is asymptotically stable as long as the delay is within the bound. The corresponding output feedback result is also derived.     

On stabilization by means of the Energy-Casimir method

Recently a stabilization result on the angular velocity equations of the rigid body has been derived by means of the Energy-Casimir method. In this paper an alternative derivation of this result is given based on a topological condition on the level surfaces defined by the constants of motion. This condition is then reinterpreted, leading to a relaxed form of the Energy-Casimir theorem. The theorem is applied to the angular velocity equations of a rigid body.     

Dynamical Output Feedback Stabilization Of Mimo Bilinear Systems With Undamped Natural Response

This paper considers the globally asymptotic stabilization problem of multi‐input multi‐output bilinear systems with undamped natural response. Under the conditions for asymptotic stabilization by static state feedback control and system detectability, two output dynamic feedback controllers with saturation bounded control are constructed. The global asymptotic stability of the closed‐loop system is verified by Lyapunov stability theory and LaSalle's Lemma. An example is given to demonstrate the obtained results.