Stability analysis of switched time delay systems

This paper addresses the asymptotic stability of switched time delay systems with heterogeneous time invariant time delays. Piecewise Lyapunov-Razumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of an infinite number of switchings. We provide sufficient conditions in terms of the minimum dwell time to guarantee asymptotic stability under the assumptions that each switching candidate is delay-independently or delay-dependently stable. Conservatism analysis is also provided by comparing with the dwell time conditions for switched delay-free systems. Finally, a numerical example is given to validate the results. © 2008 Society for Industrial and Applied Mathematics

Stability analysis of switched time-delay systems

This paper addresses the asymptotic stability of switched time delay systems with heterogenous time invariant time delays. Piecewise Lyapunov-Razumikhin functions are introduced for the switching candidate systems to investigate the stability in the presence of infinite number of switchings. We provide sufficient conditions in terms of the minimum dwell time to guarantee asymptotic stability under the assumptions that each switching candidate is delay-independently or delaydependently stable. Conservatism analysis is also provided by comparing with the dwell time conditions for switched delay free systems. © 2008 IEEE

Stability and dwell time analysis of switched time delay systems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2007.Thesis (Master's) -- Bilkent University, 2007.Includes bibliographical references leaves 59-61In this thesis we deal with stability analysis of switched feedback system with time delays. We assume that, at any given time for each “candidate” system a controller is designed and a fixed feedback system is obtained until the next switching instant. We investigate the conservativeness of an LMI-based stability test for the time delay systems. This test is used for the dwell time analysis. After obtaining the limitations of this test, we find the exact bounds of allowable parameters appearing in the LMI-based test, in order to optimize the dwell time. For this purpose we consider simple first order systems and higher order systems separately. We also consider the LQR-based switched feedback controllers with time delays and investigate the effects of weighting matrices Q and R on the dwell time.Tapkan, Osman SiraceddinM.S

Stability analysis and controller design for switched time-delay systems

In this thesis, the stability analysis and control synthesis for uncertain switched time-delay systems are investigated. It is known that a wide variety of real-world systems are subject to uncertainty and also time-delay in their dynamics. These characteristics, if not taken into consideration in analysis and synthesis, can lead to important problems such as performance degradation or instability in a control system. On the other hand, the switching phenomenon often appears in numerous applications, where abrupt change is inevitable in the system model. Switching behavior in this type of systems can be triggered either by time, or by the state of the system. A theoretical framework to study various features of switched systems in the presence of uncertainty and time-delay (both neutral and retarded) would be of particular interest in important applications such as network control systems, power systems and communication networks. To address the problem of robust stability for the class of uncertain switched systems with unknown time-varying delay discussed above, sufficient conditions in the form of linear matrix inequalities (LMI) are derived. An adaptive switching control algorithm is then proposed for the stabilization of uncertain discrete time-delay systems subject to disturbance. It is assumed that the discrete time-delay system is highly uncertain, such that a single fixed controller cannot stabilize it effectively. Sufficient conditions are provided subsequently for the stability of switched time-delay systems with polytopic-type uncertainties. Moreover, an adaptive control scheme is provided to stabilize the uncertain neutral time-delay systems when the upper bounds on the system uncertainties are not available a priori . Simulations are provided throughout the thesis to support the theoretical result

Delay-Dependent Stability Analysis of TS Fuzzy Switched Time-Delay Systems

This paper proposes a new approach to deal with the problem of stability under arbitrary switching of continuous-time switched time-delay systems represented by TS fuzzy models. The considered class of systems, initially described by delayed differential equations, is first put under a specific state space representation, called arrow form matrix. Then, by constructing a pseudo-overvaluing system, common to all fuzzy submodels and relative to a regular vector norm, we can obtain sufficient asymptotic stability conditions through the application of Borne and Gentina practical stability criterion. The stability criterion, hence obtained, is algebraic, is easy to use, and permits avoiding the problem of existence of a common Lyapunov-Krasovskii functional, considered as a difficult task even for some low-order linear switched systems. Finally, three numerical examples are given to show the effectiveness of the proposed method

Robust Stability Analysis and Synthesis for Switched Discrete-Time Systems with Time Delay

The problems of robust stability analysis and synthesis for a class of uncertain switched time-delay systems with polytopic type uncertainties are addressed. Based on the constructive use of an appropriate switched Lyapunov function, sufficient linear matrix inequalities (LMIs) conditions are investigated to make such systems a uniform quadratic stability with an L2-gain smaller than a given constant level. System synthesis is to design switched feedback schemes, whether based on state, output measurements, or by using dynamic output feedback, to guarantee that the corresponding closed-loop system satisfies the LMIs conditions. Two numerical examples are provided that demonstrate the efficiency of this approach

Delay-Dependent Stability Analysis for Uncertain Switched Time-Delay Systems Using Average Dwell Time

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched timedelay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method

Qualitative Studies of Nonlinear Hybrid Systems

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance. The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems. Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior. Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems. Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay. Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions. Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results