We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-li...

The constrained stabilization of linear uncertain systems is investigated via the set-theoretic framework of control Lyapunov R-functions. A novel composition rule allows the design of a composite control Lyapunov function with external level set that exactly shapes the maximal controlled invariant set and inner sublevel sets arbitrarily close to any choice of smooth ones, generalizing both pol...

This paper studies the control synthesis problem of Takagi–Sugeno (T–S) fuzzy systems. By splitting the premise variable spaces and using the properties of fuzzy sets, a new control scheme is proposed based on a new class of fuzzy Lyapunov functions, and a convex condition for designing fuzzy controllers is given, where the new fuzzy Lyapunov functions and fuzzy controllers are constructed base...

This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of R, then there exists a polynomial Ly...

The paper studies convex Lyapunov functions for differential and difference inclusions with right-hand sides given by convex processes, that is, by set-valued mappings the graphs of which are convex cones. Convex conjugacy between weak Lyapunov functions for such inclusions and Lyapunov functions for adjoint inclusions is established. Asymptotic stability concepts are compared and the existence...

The discrete dynamics generated by a continuous map can be represented combinatorially by an appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. In this paper we provide explicit algorithms and computational complexity bounds for computing dynamical structures for the resulting combinatorial multivalued maps. Specifically we focus on the c...

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the calculation of the Lyapunov spectrum is attributed to the eigenvalue problem of 16× 16 reduced matrices regardless of the number of particles. We show that th...

We consider an arbitrary number of interconnected nonlinear systems with time-delays and investigate them in view of input-to-state stability (ISS). The useful tools for single time-delay systems, the ISS Lyapunov-Razumikhin functions and ISS Lyapunov-Krasovskii functionals are redefined and applied to interconnected systems. By the help of a smallgain condition we prove that the whole system w...

This paper addresses two strategies for stabilization of continuous time linear switched system. The first one, is of open loop nature (trajectory independent) and is based on the determination of a minimum dwell time by means of a family of quadratic Lyapunov functions. Interestingly, the proposed stability condition does not require the Lyapunov function be uniformly decreasing at every switc...

in this paper, a robust pid control scheme is proposed for micro-electro-mechanical-systems(mems) optical switches. the proposed approach is designed in a way which solves twochallenging and important problems. the first one is successful reference tracking and the second ismitigating the system nonlinearities. the overall system composed of nonlinear mems dynamicsand the pid controller is prov...