Periodic stabilizability of switched linear control systems

Stabilizability via direct/observer-based state feedback control for discrete-time switched linear control systems (SLCSs) is investigated in this paper. For an SLCS, the control factors are not only the control input but also the switching signal, and they need to be designed in order to stabilize the system. As a result, stabilization design for SLCSs is more complicated than that for non-switched ones. Differently from the existing approaches, a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems. It is highlighted that multiple feedback controllers need to be designed for one subsystem. For discrete-time SLCSs, it is proved that reachability implies periodic stabilizability via state feedback. A necessary and sufficient criterion for periodic stabilizability is also established. Two stabilization design algorithms are presented for real application. Moreover, it is proved that reachability and observability imply periodic stabilizability via observer-based feedback for discrete-time SLCSs. Periodic detectability, as the dual concept of periodic stabilizability, is discussed and the stabilization design algorithms via observer-based feedback are presented as well.     

Detectability for Nondeterministic Discrete Event Systems and Its Applications in Medical Diagnosis

In this paper, we extend our previous results on detectability to nondeterministic discrete event systems. Many practical systems are nondeterministic, especially those in biomedicine. Disease models of patients are usually nondeterministic because hardly anything is deterministic in biological systems. The goal is to determine or estimate the current and subsequent states of a system based on a sequence of observations when the initial state of the system is unknown. We say that a system is detectable if one can determine its state after observing some outputs. The observation includes partial event observation and/ or partial state observation. We define four types of detectabilities： strong detectability, （weak） detectability, strong periodic detectability, and （weak） periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observation. Furthermore, we apply the results to medical diagnosis by considering a realistic example of diagnosing whether a patient suffers from one of the following five similar diseases ： （ 1 ） rheumatoid arthritis, （2） rheumatic arthritis, （ 3 ） systemic lupus eruthematosus, （4） bony ankylosis, or （ 5 ） spondylitis ankylopoietica.     

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.     

High order sliding mode observer for linear systems with unbounded unknown inputs

A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is generated in order to fulfil, what we will call, the Hautus condition, which finally allows decomposing the system, in new coordinates, into two subsystems; the first one being unaffected directly by the unknown inputs, and the state vector of the second subsystem is obtained directly from the original system output. Such decomposition permits designing of a Luenberger observer for the first subsystem, which satisfies the Hautus condition, i.e. all the outputs have relative degree one w.r.t. the unknown inputs. This procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible. Simulations are given in order to show the effectiveness of the proposed observer.     

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.     

A method of robust multi-rate state estimation

The inadequacy of the standard notions of detectability and observability to ascertain robust state estimation is shown. The notion of robust state estimation is defined, and for a class of processes the conditions under which the robust state estimation is possible, are given. A method of robust, nonlinear, multi-rate, state estimator design is presented. It can be used to improve robustness in an existing estimator or design a new robust estimator. Estimator tuning guidelines that ensure the asymptotic stability of the estimator error dynamics are given. To ensure that estimation error does not exceed a desired limit, the sampling period of infrequent measurements should be less than an upper bound that depends on factors such as the size of the process dominant time constant, the magnitude of measurement noise, and the level of process–model mismatch. An expression that can be used to calculate the upper bound on the sampling period of infrequent measurements, is presented. The upper bound is the latest time at which the next infrequent measurements should arrive to ensure that estimation error does not exceed a desired limit. The expression also allows one to calculate the highest quality of estimation achievable in a given process. A binary distillation flash tank and a free-radical polymerization reactor are considered to show the application and performance of the estimator.     

射线实时成像检验技术与射线照相检验技术的等价性讨论

在分析射线照相检验技术的有关规定的基础上，提出了射线实时成像检验技术在与射线照相检验技术具有同等缺陷检验能力情况下的等价性指标。对射线实时成像检验技术的应用具有重要意义。     

Sontag's ‘input to state stability condition’ and global stabilization using state detection

This paper deals with the global stabilization problem for nonlinear system using state detection. Sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included. These conditions are based to a version of a Lyapunov-like condition proposed by Sontag, which guarantees ‘input to state stability’.     

Further results on the observer design problem

In this paper the observer design problem for nonlinear systems is considered. Sufficient Lyapunov-like conditions are presented for the existence of a nonlinear observer. The theory we develop considerably improves and extends the results of our recent work [14].     

A review of factors influencing defect detection in infrared thermography: Applications to coated materials

Infrared thermography is a technique that is used to nondestructively inspect parts for the presence of subsurface defects. The technique normally consists of applying heat to one surface of the part and observing the thermal response, using heat-sensing devices such as infrared cameras, as the part cools. Internal defects such as voids modify the thermal response and produce local hot or cold spots on the specimen surface. For the detection of subsurface defects, the sensitivity of the technique to different parameters such as defect depth, material properties, and heating methods has not been established due in part to the complex nature of the heat/flaw interaction. A finite element model is used here to examine the influence of these parameters on defect dectability. The model shows that the defect detectability decreases with increasing defect depth beneath the surface, and that the technique is most sensitive to the inspection of low thermal diffusivity coatings bonded to high thermal diffusivity substrates. The results also show that the heat pulse duration should be made as short as possible to maximize defect detectability.