区间线性脉冲系统的鲁棒耗散性及其反馈镇定

主要讨论了区间线性脉冲系统相对于二次供给率的鲁棒耗散性问题, 得到了该系统是鲁棒耗散的充分条件, 而且还给出了这样的鲁棒耗散系统能被一个状态反馈控制律所镇定的条件, 最后, 给出了一个例子.     

Robust decentralized stabilization for a class of large-scale time-delay uncertain impulsive dynamical systems

The problem of robust decentralized stabilization for a class of large-scale, time delay, and uncertain impulsive dynamical systems is introduced and studied. Some explicit criteria of robust exponential stabilization in the large for such systems are established. A simple approach to designing a robust decentralized controller is presented. A numerical example is given for illustrating and interpreting the theoretical results.     

An impulsive dynamical systems framework for reset control systems

Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyse several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence on the initial condition (well-posedness). The work scope is about reset control systems with a linear and time-invariant base system, and a zero-crossing resetting law. A necessary and sufficient condition for existence and uniqueness of solutions, based on the well-posedness of reset instants, is developed. As a result, it is shown that reset control systems (with strictly proper plants) do not have Zeno solutions. It is also shown that full reset and partial reset (with a special structure) always produce well-posed reset instants. Moreover, a definition of continuous dependence on the initial condition is developed, and also a sufficient condition for reset control systems to satisfy that property. Finally, this property is used to analyse sensitivity of reset control systems to sensor noise. This work also includes a number of illustrative examples motivating the key concepts and main results.     

Robust stabilization of uncertain impulsive switched systems with delayed control

In this paper, stability criteria and switching controllers’ design problems for uncertain impulsive switched systems with input delay are investigated by using the receding horizon method. Some LMI conditions are derived to guarantee asymptotical stability of an impulsive switched system under a certain designed delayed controller. Finally, a numerical example is presented to illustrate the effectiveness of the results obtained.     

Feedback stabilization of discrete-time homogeneous semi-linear systems

For discrete-time semi-linear systems satisfying an accessibility condition asymptotic null controllability is equivalent to exponential feedback stabilizability using a piecewise constant feedback. A constructive procedure that yields such a feedback is presented.     

Constructive stabilization for quadratic input nonlinear systems

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.     

Quadratic stabilization of switched systems

We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched system is quadratically stabilizable via switched state feedback for all uncertainties.     

Quadratic stability and stabilization of bimodal piecewise linear systems

This paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems. First, we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems. Later, these conditions are investigated from a geometric control point of view and a set of sufficient conditions (in terms of the zero dynamics of one of the two linear subsystems) for feedback stabilization are obtained.     

Global stabilization of discrete-time homogeneous systems

The feedback stabilization of continuous time Δ^r-homogeneous systems has been studied by several authors, see for instance (Dayawansa and Martin, Proceedings of the 28th C.D.C., Tampa, Florida, December, 1989, Hermes, J. Differential Equations 92 (1991) 76–89, Hermes, Systems Control Lett. 24 (1995) 7–11, Kawski, Proceedings of the 27th C.D.C., Texas, 1988, Texas, Kawski, Control Theory and Advanced Technology, vol. 6, MITA Press, Tokyo, 1996, pp. 497–516, Sepulchre and Aeyels, Math. Control Signal Systems 9 (1996) 34–58). In (Kawski, Analysis of Controlled Dynamical Systems, Birkhauser, Basel, 1991, Kawski, Proceedings of IFAC NOLCOS, 1995), Kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations. In this note, we define the homogeneity of transition maps w.r.t. continuous dilations and we show how one can construct a global stabilizing feedback control for discrete-time homogeneous systems which are locally asymptotically stabilizable.     

Reliable dissipative control for stochastic impulsive systems

This paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems. The systems under study are subject to Markovian jump, parameter uncertainties, possible actuator failure and impulsive effects, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly (Q,S,R)-dissipative. The sufficient conditions are obtained by using linear matrix inequality (LMI) techniques. The main results of this paper extend the existing results on H^∞ control.     

Robust stabilization of nonlinear cascaded systems

This paper considers the problem of robust stabilization for an uncertain nonlinear system which is a cascaded interconnection of two subsystems. Both of the subsystems are allowed to be nonlinear, multi-variable, and containing uncertain parameters. We present a new approach to designing stabilizing controllers which assure both robust global asymptotic stability and local quadratic stability. Compared with existing results, the assumptions required for such robust stabilizing controllers to exist are significantly simplified.     

Exponential stabilization for nonlinear coupled dynamical systems via impulsive and sampled‐data control with input constraints

In this paper, exponential stabilization for nonlinear coupled dynamical systems by considering sampled‐data controller and impulsive controller with input constraints is investigated. Based on polytopic representation approach, some linear matrix inequalities are established to guarantee local exponential stabilization of nonlinear coupled dynamical systems. Moreover, by using polytopic differential inclusion, for the case of the partial input saturation involving in the impulsive controller, we also obtain several sufficient conditions ensuring local exponential stabilization. Finally, three examples are presented to show the effectiveness of theoretical analysis.     

Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control

This paper derives a feedback controlf(t), ‖f(t)‖_E≦r,r>0, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=u _o ≠H to have the asymptotic behavioru(t)→0 ast→∞ inH. HereA is the infinitesimal generator of aC _o semigroup of contractionse ^At on a real Hilbert spaceH andB is a bounded linear operator mapping a Hilbert space of controlsE intoH. An application to the boundary feedback control of a vibrating beam is provided in detail and an application to the stabilization of the NASA Spacecraft Control Laboratory is sketched. This research was sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF Contract/Grants AFOSR 81-0172 and AFOSR 87-0315.     

A unified synchronization criterion for impulsive dynamical networks

This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named “average impulsive interval”. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.     

Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays

We consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured observable are thus the open-loop stationary states: they are used to construct a closed-loop supermartingale playing the role of a strict control Lyapunov function. The parameters of this supermartingale are calculated by inverting a Metzler matrix that characterizes the impact of the control input on the Kraus operators defining the Markov process. The resulting state feedback scheme, taking into account a known constant delay, provides the almost sure convergence to the target state. This convergence is ensured even in the case where the filter equation results from imperfect measurements corrupted by random errors with conditional probabilities given as a left stochastic matrix. Closed-loop simulations corroborated by experimental data illustrate the interest of such nonlinear feedback scheme for the photon box, a cavity quantum electrodynamics system.     

Input-to-state stability of impulsive and switching hybrid systems with time-delay

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov–Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in the ISS/iISS sense, provided that there are no overly long intervals between impulses, i.e., the impulsive and switching signal satisfies a dwell-time upper bound condition. Moreover, these impulsive ISS/iISS stabilization results can be applied to systems with arbitrarily large time-delays. Conversely, in the case when all the subsystems governing the continuous dynamics are ISS/iISS in the absence of impulses, the ISS/iISS properties can be retained if the impulses and switching do not occur too frequently, i.e., the impulsive and switching signal satisfies a dwell-time lower bound condition. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

Feedback stabilization of real analytic systems in the plane

We investigate the local feedback stabilization of single input control affine analytic systems in the plane. New necessary and sufficient conditions for local stabilization with feedback laws of the form u = v(x₁,x₂), x2), (v/x₁(0, 0))² + (v/x₁ (0, 0))² 0≠ 0, v(0, 0) = 0, are obtained by using Lyapunov's stability theorems on two-dimensional analytic systems. If the sufficient conditions are satisfied, we also provide explicit feedback laws.