We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., ...

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapuno...

In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a “hybrid” control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, whil...

The consistent Lyapunov methodology enables us, after its single application, to solve completely the asymptotic (or, exponential) stability problem, to construct a system Lyapunov function and to determine accurately the domain of asymptotic stability. This is achieved in the paper for invariant sets of non-differentiable time-varying non-linear systems. The results (proved in details) present...

We use discrete quadratic Lyapunov functions to design controllers for a class of systems where time intervals between state measurements are longer than time intervals between control actions and different components of the state vector are not measured at the same time. The discrete Lyapunov function is a discretization of a continuous Lyapunov function assumed to be known for the idealized s...

We present a method for the construction of Foster-Lyapunov functions to prove ergodicity of hybrid piecewise-deterministic Markov processes. Our method searches for the Lyapunov function that maximizes a measure of the rate of convergence that appears in the theory of large deviations. We provide conditions under which such a Lyapunov function is the limit of an iterative procedure. Analytical...

This paper deals with the problem of reliable guaranteed cost control for linear descriptor time-delay systems with actuator failure. The actuator failure mold adopted in this paper is in complete form to describe variation of the actuator. To design a controller such that, for admissible actuator failures, the plant remains asymptotically stable and guarantees an adequate level of a quadratic ...

We propose discrete mappings of second order that have a discrete analogue of Lyapunov function. The mappings are extensions of the integrable Quispel-RobertsThompson (QRT) mapping, and a discrete Lyapunov function of the mappings is identical to an explicit conserved quantity of the QRT mapping. Moreover we can obtain a differential and an ultradiscrete limit of the mappings preserving the exi...

We study families of time-varying linear systems with restrictions on the derivative of the parameter variation. This includes the systems usually considered in the area of linear parameter varying (LPV) systems. We show that it is possible to construct exact parameterized Lyapunov norms for a wide class of such systems. This may be used to derive (locally Lipschitz) continuous dependence of th...