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This paper studies the consensus problem of nonidentical Euler–Lagrange systems with parametric uncertainties, under switching directed graphs. We present an adaptive distributed control algorithm that solves this problem in the leaderless scenario, under weak assumptions on the switching interconnection between agents. It is shown that the proposed consensus protocol achieves consensus without using neighbor's velocity information and accounts for the discontinuity of the input torque that results from the switching interaction between agents. Simulation results are given to illustrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper proposes a novel switched second order sliding mode (S-SOSM) control strategy, which allows enhancing the closed-loop performance and tune the system behavior to the current working condition. Such a control approach is intended to deal with systems characterized by different levels of uncertainties associated with different regions of the state space and to accommodate different control objectives in the different regions, so as to improve transient performance and robustness by switching among appropriate SOSM controllers. The proposed control approach allows one to improve the transient performance by switching among appropriate SOSM controllers associated with each region of the state space, with only a modest increase in the controller complexity. It is shown that the proposed control algorithms ensure global finite-time convergence to the origin of the closed-loop state trajectory. The validity of the proposed approach is analysed on a realistic case study addressing the wheel slip control of two-wheeled vehicles. [ABSTRACT FROM AUTHOR]

This paper presents a characterization of observability and an observer design method for switched linear systems with state jumps. A necessary and sufficient condition is presented for observability, globally in time, when the system evolves under predetermined mode transitions. Because this characterization depends upon the switching signal under consideration, the existence of singular switching signals is studied alongside developing a sufficient condition that guarantees uniform observability with respect to switching times. Furthermore, while taking state jumps into account, a relatively weaker characterization is given for determinability, the property that concerns with recovery of the original state at some time rather than at all times. Assuming determinability of the system, a hybrid observer is designed for the most general case to estimate the state of the system and it is shown that the estimation error decays exponentially. Since the individual modes of the switched system may not be observable, the proposed strategy for designing the observer is based upon a novel idea of accumulating the information from individual subsystems. Contrary to the usual approach, dwell-time between switchings is not necessary, but the proposed design does require persistent switching. For practical purposes, the calculations also take into account the time consumed in performing computations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate distributed multi-agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities. Various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking. Based on the connectivity of the time-varying multi-agent system, necessary and sufficient conditions are obtained for set input-to-state stability and set integral input-to-state stability for a nonlinear neighbor-based coordination rule with switching directed topologies. Conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders. [ABSTRACT FROM AUTHOR]

This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter. [ABSTRACT FROM AUTHOR]

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (finite) family of given configurations (Ai, Bi, Ci). We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current configuration i. As a first result, we provide necessary and sufficient conditions for the existence of a switching compensator such that the closed-loop plant is stable under arbitrary switching. These conditions are based on a separation principle, precisely, the switching stabilizing control can be achieved by separately designing an observer and an estimated state (dynamic) compensator. These conditions are associated with (non-quadratic) Lyapunov functions. In the quadratic framework, similar conditions can be given in terms of LMIs which provide a switching controller which has the same order of the plant. As a second result, we furnish a characterization of all the stabilizing switching compensators for such switching plants. We show that, if the necessary and sufficient conditions are satisfied then, given any arbitrary family of compensators Ki(s), each one stabilizing the corresponding LTI plant (Ai, Bi, Ci) for fixed i, there exist suitable realizations for each of these compensators which assure stability under arbitrary switching. [ABSTRACT FROM AUTHOR]

We study optimization-based criteria for the stability of switching systems, known as path-complete Lyapunov functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another?”. Our contribution is twofold. First, we show that a path-complete Lyapunov function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each path-complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given path-complete Lyapunov functions. [ABSTRACT FROM AUTHOR]

The agreement control problem of single and double-integrator agents with unknown and nonidentical control directions is addressed in this note under switching network topology. Distributed nonlinear PI control laws are proposed which ensure asymptotic consensus among the agents based on a new boundedness lemma and a generalized version of Barbalát's lemma for uniformly piecewise right continuous functions. Theoretical results are verified by simulation studies. [ABSTRACT FROM AUTHOR]

This article deals with stability of continuous-time switched systems under constrained switching. Given a family of systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which the switched system generated by it and the family of systems is globally asymptotically stable. Our characterization of such stabilizing switching signals involves the asymptotic frequency of switching, the asymptotic fraction of activation of the constituent systems, and the asymptotic densities of admissible transitions among them. Our techniques employ multiple Lyapunov-like functions, and extend preceding results both in scope and applicability. [ABSTRACT FROM PUBLISHER]

A new linear method for solving the output feedback pole assignment problem of linear systems is introduced, and new sufficient conditions are obtained. [ABSTRACT FROM AUTHOR]

We present an optimal control framework for persistent monitoring problems where the objective is to control the movement of multiple cooperating agents to minimize an uncertainty metric in a given mission space. In a 1-D mission space, we show that the optimal solution is for each agent to move at maximal speed from one switching point to the next, possibly waiting some time at each point before reversing its direction. Thus, the solution is reduced to a simpler parametric optimization problem: determining a sequence of switching locations and associated waiting times at these switching points for each agent. This amounts to a hybrid system which we analyze using infinitesimal perturbation analysis (IPA) to obtain a complete on-line solution through a gradient-based algorithm. We also show that the solution is robust with respect to the uncertainty model used. This establishes the basis for extending this approach to a two-dimensional mission space. [ABSTRACT FROM AUTHOR]

A state-dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed. Sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each subsystem such that it is non-increasing at the switching instants. During the dwell time, this function varies piecewise linearly in time. After the dwell, the system switches if the switching results in a decrease in the value of the LF. The method proposed is also applicable to robust stabilization via state-feedback. It is further extended to guarantee a bound on the \cal L2-gain of the switching system; it is also used in deriving state-feedback control law that robustly achieves a prescribed \cal L2-gain bound. [ABSTRACT FROM AUTHOR]

An adaptive approach is proposed to address the problem of robustification (and performance loss reduction) of anti-windup (AW) compensation in the presence of large uncertainties. The approach relies on the augmentation of the AW compensator with an adaptive robustifying filter; a constructive procedure is provided for designing such a filter. The use of adaptation allows to reduce the conservativeness of previous robust approaches to what is needed to preserve stability with respect to the uncertainty actually present on the plant during operation, as detected by input and output plant measurement. [ABSTRACT FROM AUTHOR]

This technical note addresses the problem of observability of continuous—time Switched Linear Systems (SLS) subject to unknown disturbances, unknown switching signals and unconstrained nonzero dwell time. For this class of hybrid systems, a geometric characterization of the observability properties is presented. In particular, attention is focused on the estimation of the SLS state from the continuous measurements. [ABSTRACT FROM AUTHOR]

Synchronization in complex networks with time dependent coupling and stochastically switching coupling structure is discussed. A novel approach investigating synchronization based on the scramblingness property of the coupling matrix is proposed. Some sufficient condition for a network with general time-varying coupling structure to reach complete synchronization is provided. Based on the general theorem, networks with stochastically switching coupling structures is investigated. In particular, two kinds of stochastic switching coupling networks are addressed: (a) independent and identically distributed switching processes and (b) Markov jump processes. In both cases, some sufficient condition for almost sure synchronization of the networks is given. Also, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this note, we investigate the stabilization of switched systems with nonlinear impulse effects and disturbances. Based on the estimate on transition matrices and Gronwall inequality, feedback laws are designed to achieve the exponential stability of the closed-loop system with arbitrary switching frequency. [ABSTRACT FROM AUTHOR]

This technical note addresses the stabilization of switching discrete-time linear systems with control inputs under arbitrary switching. A sufficient condition for the uniform global exponential stability (UGES) of such systems is the existence of a common quadratic Lyapunov function (CQLF) for the component subsystems, which is ensured when the closed-loop component subsystem matrices are stable and generate a solvable Lie algebra. The present work develops an iterative algorithm that seeks the feedback maps required for stabilization based on the previous Lie-algebraic condition. The main theoretical contribution of the technical note is to show that this algorithm will find the required feedback maps if and only if the Lie-algebraic problem has a solution. The core of the proposed algorithm is a common eigenvector assignment procedure, which is executed at every iteration. We also show how the latter procedure can be numerically implemented and provide a key structural condition which, if satisfied, greatly simplifies the required computations. [ABSTRACT FROM AUTHOR]

Inspired by prior work in the design of switched feedback controllers for second-order systems, we develop a switched state feedback control law for the stabilization of linear time-invariant (LTI) systems of arbitrary dimension. The control law operates by switching between two static gain vectors in such a way that the state trajectory is driven onto a stable n-1 dimensional hyperplane (where n represents the system dimension). We begin by briefly examining relevant geometric properties of the phase portraits in the case of two-dimensional systems to develop intuition, and we then show how these geometric properties can be expressed as algebraic constraints on the switched vector fields that are applicable to LTI systems of arbitrary dimension. We then derive necessary and sufficient conditions to ensure stabilizability of the resulting switched system using the proposed approach (characterized primarily by simple conditions on eigenvalues) and describe an explicit procedure for designing stabilizing controllers. We then show how the newly developed control law can be applied to the problem of minimizing the maximal Lyapunov exponent of the corresponding closed-loop state trajectories, and we illustrate the closed-loop transient performance of these switched state feedback controllers via multiple examples. [ABSTRACT FROM AUTHOR]

Sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, which is non-increasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs. It becomes time invariant afterwards. This function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties. The method proposed is then applied to stabilization via state-feedback both for the nominal and the uncertain cases. [ABSTRACT FROM AUTHOR]

Hybrid dynamical systems consist of both continuous-time and discrete-time dynamics. A fundamental phenomenon that is unique to hybrid systems is Zeno behavior, where the solution involves an infinite number of discrete transitions occurring in finite time, as best illustrated in the classical example of a bouncing ball. In this note, we study the hybrid system of the set-valued bouncing ball, for which the continuous-time dynamics has a set-valued right-hand side. This system is typically used for deriving bounds on the solution of nonlinear single-valued hybrid systems in a small neighborhood of a Zeno equilibrium point in order to establish its local stability. We utilize methods of Lyapunov analysis and optimal control to derive a necessary and sufficient condition for Zeno stability of the set-valued bouncing ball system and to obtain a tight bound on the Zeno time as a function of initial conditions. [ABSTRACT FROM AUTHOR]

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in Rnxn are stable. In particular, we are interested whether there exist algorithms which can solve this problem in time polynomial in n and k. We show that if k = [nd] for any fixed real d > 0, then the problem is NP-hard, meaning that no polynomial-time algorithm in n exists provided that P ≠ NP, a widely believed conjecture in computer science. On the other hand, when k is a constant independent of n, then it is known that the problem may be solved in polynomial time in n. Using these results and the method of measurable switching rules, we prove our main statement: verifying the absolute asymptotic stability of a continuous-time switched linear system with more than nd matrices Ai ϵ Rnxn satisfying 0 ≽ Ai + AiT is NP-hard. [ABSTRACT FROM AUTHOR]

A set of switching sequences of a discrete-time switched linear system is said to be uniformly stabilizing if the system is uniformly exponentially stable over all switching sequences that belong to the set. Based on the recent result that a switched linear system is uniformly stable if and only if an increasing countable union of linear matrix inequality conditions is satisfied, we characterize all uniformly stabilizing sets of switching sequences. A discrete-time hybrid automaton of the automobile engine is considered to illustrate the result. [ABSTRACT FROM AUTHOR]