Stability and Observer Design for Lur'e Systems with Multivalued, Nonmonotone, Time-Varying Nonlinearities and State Jumps

Math. Control Signals Syst.

2015

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We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive Lyapunov-based conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions are based on the stability margin of the Lebesgue-integrable and the measure-driven components of the system. For more general inputs which do not necessarily lead to asymptotic stability, we then derive conditions such that the maximum norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems.

Section: Contributionmentioning

confidence: 99%

Stability notions for a class of nonlinear systems with measure controls

Math. Control Signals Syst.

2015

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“…For brevity, we have suppressed the time argument in (22), and will do so in the remainder of this section unless required. Let us also introduce the following notation:…”

Section: Error Feedback and Dynamic Compensatormentioning

confidence: 99%

On output regulation in systems with differential variational inequalities

53rd IEEE Conference on Decision and Control

2014

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We consider the problem of designing state feedback control laws for output regulation in a class of dynamical systems which are described by variational inequalities and ordinary differential equations. In our setup, these variational inequalities are used to model state trajectories constrained to evolve within time-varying, closed, and convex sets, and systems with complementarity relations. We first derive conditions to study the existence and uniqueness of solutions in such systems. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. 53rd IEEE Conference on Decision and Control

“…In this regard, we mention the recent work on observer design of switched systems with ordinary differential equations [34], [38], [39], switched differential-algebraic equations [40], [41], certain classes of differential inclusions [10], [29], [36], complementarity systems [17], and the references therein for more details. Classical approaches for observer design are based on constructing an auxiliary dynamical system driven by the error between the measured output and the estimated output, where it is shown that the resulting dynamics of the state estimation error converge to the origin.…”

Section: Introductionmentioning

confidence: 99%

Observer Design for Unilaterally Constrained Lagrangian Systems: A Passivity-Based Approach

IEEE Trans. Automat. Contr.

2016

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Abstract-This paper addresses the problem of state estimation in nonlinear Lagrangian dynamical systems with frictionless unilateral constraints using the position measurement as output. The discontinuous velocity variable in such systems is modeled as a function of bounded variation (so that Zeno phenomenon is not ruled out). Since the derivative of such functions is represented with the Lebesgue-Stieltjes measure, the framework of measure differential inclusions (MDIs) is used to describe the dynamics. A class of estimators is proposed, which also uses the framework of MDIs, and is shown to generate asymptotically converging state estimates. The existence and uniqueness of solutions for the proposed estimators is rigorously proven. The global stability of error dynamics is analyzed using the generalized Lyapunov methods for functions of bounded variation. As particular cases of our estimators, we provide an explicit construction of a full-order observer, and a reduced-order observer.Index Terms-Complementarity systems, functions of bounded variation, convex analysis, systems with impacts, Lagrangian systems, Lyapunov methods, Moreau's sweeping process, observers, state estimation.