Stability of sampled-data piecewise-affine systems under state feedback

This paper addresses stability of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. The paper presents conditions under which the trajectories of the sampled-data closed-loop system will exponentially converge to a neighborhood of the origin. Moreover, the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure, in particular, related to the sampling period. Finally, it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous-time PWA state feedback controller can be recovered by the emulated controller.     

Delay-dependent sampled-data control based on delay estimates

In this paper the sampled-data stabilization of linear time-invariant systems with feedback delay is considered. We assume that the delay is time-varying and that its value is approximatively known. We investigate how to use the available information about the evolution of delays for adapting the control law in real time. Numerical methods for the design of a delay-dependent controller are presented. This allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure.     

变周期采样系统指数稳定的新条件

本文研究了线性采样系统在变周期采样下的指数稳定性问题.基于离散时间Lyapunov理论,构造了一个新的类Lyapunov泛函.该泛函不仅是时变的,还增加了对状态二次项的积分,而且不要求在采样区间内正定.利用这一新的类Lyapunov泛函,本文首先针对一类非线性采样系统提出了指数稳定性定理,再结合改进的Wirtinger积分不等式,导出了使变周期线性采样系统指数稳定以及渐近稳定的线性矩阵不等式条件.最后举例说明了所得稳定性结果比现存的某些文献报道的结果保守性较小.     

Stability analysis of Markovian jump systems with delayed impulses

This paper addresses stability for Markovian jump systems with delayed impulses. The delayed impulse has a largely negative effect on the system stability and is not easy to be studied. The main reason is that so many factors such as Markovian switching, impulse, and time-varying delay are simultaneously contained and make its analysis complicated and difficult. In order to analyze these factors clearly, some novel enlarging techniques are presented and used to establish linear matrix inequality (LMI) conditions ultimately. Based on the given methods, more situations such as impulsive instant sequence satisfying a renewal process and Poisson process, respectively, are further studied and better than ones without considering such properties. Two numerical examples are used to show the effectiveness and superiority of the methods.     

Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities

Stability analysis of an aperiodic sampled-data control system is considered for application to networked and embedded control. The stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals. Although this condition is numerically intractable, a tractable sufficient condition can be constructed with the mean value theorem. Special attention is paid to tightness of the sufficient condition for less conservative stability analysis. A region-dividing technique for the reduction of conservatism and generalization to stabilization are also discussed. An example demonstrates the efficacy of the approach.     

Stability and stabilization of nonuniform sampling systems

This paper is concerned with nonuniform sampling systems, where the sampling interval is time-varying within a certain known bound. The system is transformed into a time-varying discrete time system, where time-varying parts due to the sampling interval variation are treated as norm bounded uncertainties using robust control techniques. To reduce conservatism arising from modeling time-varying parts as a single uncertainty, the time-varying parts are modeled as N uncertainties. With larger N, a less conservative stability condition is derived at sacrifice of more computation. It is shown through a numerical example that the proposed stability condition is better than existing stability conditions.     

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.     

Positive-realness analysis of sampled-data systems and its applications

In this paper, we first study strong positive-realness of sampled-data systems and introduce a measure called positive-realness gap index. We show that this index can be computed efficiently with a bisection method, and provide state space formulas for its computation. The importance of this index lies in that it is useful for robust stability analysis of sampled-data systems. An iterative procedure for computing an exact robust stability margin is given and illustrated through a numerical example.     

Stability analysis of nonlinear systems in the presence of event-triggered impulsive control

This note puts forward continuous event-triggered impulsive control (CETIC) and dynamic event-triggered impulsive control (DETIC) to discuss a class of (integral) input-to-state stability (iISS, ISS) for nonlinear systems (NSs), where the impulse sequences are produced by certain predesigned event-triggering conditions. Different from traditionary event-triggered control (ETC), CETIC indicates that a controller will be stimulated only if the given state-dependent event condition is invoked. There exist no transfer of control between two continuous impulse triggered instants. Compared with the traditional static ETC, the DETIC can efficaciously lessen controller update and dramatically save energy at the same decay rate. In addition, all sample path solutions (SPS) for the system have the lowest time between events guaranteed to be positive. Utilizing CETIC strategy, we get some Lyapunov conditions to effectually avoid infinite triggering behavior and obtain the ISS-type stability of the investigative systems. Then, one applies the theoretical consequences to NSs and derive a class of ETC mechanism with impulsive control gains (ICG) by linear matrix inequalities (LMIs). Because of the existence of timer, the DETIC strategy naturally excludes Zeno phenomena. Furthermore, conclusions in this thesis permit the upper bound estimation for the differential Lyapunov function coefficient to be time-varying function instead of a constant in certain extant results, which means the criteria of the Lyapunov technique in this paper is less conservative and looser. Eventually, three examples with related simulations are demonstrated to indicate the rationalization and usefulness of our conclusion.     

Stability and stabilization of linear sampled-data systems with multi-rate samplers and time driven zero order holds

In multi-rate sampled-data systems, a continuous-time plant is controlled by a discrete-time controller which is located in the feedback loop between sensors with different sampling rates and actuators with different refresh rates. The main contribution of this paper is to propose sufficient Krasovskii-based stability and stabilization criteria for linear sampled-data systems, with multi-rate samplers and time driven zero order holds. For stability analysis, it is assumed that an exponentially stabilizing controller is already designed in continuous-time and is implemented as a discrete-time controller. For each sensor (or actuator), the problem of finding an upper bound on the lowest sampling frequency (or refresh rate) that guarantees exponential stability is cast as an optimization problem in terms of linear matrix inequalities (LMIs). Furthermore, sufficient conditions for controller synthesis are formulated as LMIs. It is shown through examples that choosing the right sensors (or actuators) with adequate sampling frequencies (or refresh rates) has a considerable impact on stability of the closed-loop system.     

Synchronization for general complex dynamical networks with sampled-data

In this paper, the sampled-data synchronization control problem is investigated for a class of general complex networks with time-varying coupling delays. A rather general sector-like nonlinear function is used to describe the nonlinearities existing in the network. By using the method of converting the sampling period into a bounded time-varying delay, the addressed problem is first transformed to the problem of stability analysis for a differential equation with multiple time-varying delays. Then, by constructing a Lyapunov functional and using Jensen's inequality, a sufficient condition is derived to ensure the exponential stability of the resulting delayed differential equation. Based on that, the desired sampled-data feedback controllers are designed in terms of the solution to certain linear matrix inequalities (LMIs) that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data control scheme.     

Stability analysis of systems with aperiodic sample-and-hold devices

Motivated by the widespread use of networked and embedded control systems, improved stability conditions are derived for sampled-data feedback control systems with uncertainly time-varying sampling intervals. The results are derived by exploiting the passivity-type property of the operator arising in the input-delay approach to the system in addition to the gain of the operator, and are hence less conservative than existing ones.     

Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to the stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.     

Robust optimal control of bilinear DC-DC converters

This paper addresses the control problem of dc-dc converters. The control law synthesis considered here exploits the potential of LMI-based control approaches, which allow to cope with model uncertainty, disturbances and bilinearities to synthesize simple state-feedback controllers with a priori guarantee of stability in a large domain of initial and operating conditions. The aim of the paper is to contribute with a robust control framework to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and with experimental measurements from a laboratory prototype.     

Quantized output feedback control for networked control systems

This paper addresses the problem of output feedback control for networked control systems (NCSs) with limited communication capacity. Firstly, we propose a new model to describe the non-ideal network conditions and the input/output state quantization of the NCSs in a unified framework. Secondly, based on our newly proposed model and an improved separation lemma, the observer-based controller is developed for the asymptotical stabilization of the NCSs, which are shown in terms of nonlinear matrices inequalities. The nonlinear problems can be computed through solving a convex optimization problems, and the observed and controller gains could be derived by solving a set of linear matrix inequalities. Thirdly, two simulation examples are given to demonstrate the effectiveness of the proposed method.     

Relaxed stabilization conditions for continuous-time Takagi-Sugeno fuzzy control systems

This paper deals with the stabilization of continuous-time Takagi-Sugeno (T-S) fuzzy control systems. Based on fuzzy Lyapunov functions and nonparallel distributed compensation (non-PDC) control laws, new stabilization conditions are represented in the form of linear matrix inequalities (LMIs). The theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature. Moreover, in order to demonstrate the effectiveness of the non-PDC control laws, the problem of H_∞ controller design for T-S fuzzy systems is also studied. Simulation examples are given to illustrate the merits of the proposed methods.