One of the primary tools in establishing the stability of a fluid network is to construct a Lyapunov function. In this paper, we establish the sufficiency in the use of a Lyapunov function. Specifically, we show that a necessary and sufficient condition for the stability of a generic fluid network (GFN) is the existence of a Lyapunov function for its fluid level process. Then by applying this r...

This work proposes a neural-fuzzy sliding mode control scheme for a hydro-turbine speed governor system. Considering the assumption of elastic water hammer, a nonlinear mode of the hydro-turbine governor system is established. By linearizing this mode, a sliding mode controller is designed. The linearized mode is subject to uncertainties. The uncertainties are generated in the process of linear...

this work proposes a neural-fuzzy sliding mode control scheme for a hydro-turbine speed governor system. considering the assumption of elastic water hammer, a nonlinear mode of the hydro-turbine governor system is established. by linearizing this mode, a sliding mode controller is designed. the linearized mode is subject to uncertainties. the uncertainties are generated in the process of linear...

This note presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially...

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct expli...

This paper discusses conditions on stability and stabilization of continuous T-S fuzzy systems. Stability analysis is derived via non-quadratic Lyapunov function technique and LMIs (Linear Matrix Inequalities) formulation to obtain an efficient solution. The nonquadratic Lyapunov function is built by inference of quadratic Lyapunov function of each local model. We show that stability condition ...

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak convergence for probabilistic processes) towards their mean-field limit, i.e an ordinary differential equation (ODE) in the general case. We focus then on a cla...

One of the most fundamental results in analysing the stability properties of periodic orbits and limit cycles of dynamical systems is Poincaré’s theorem. The proof of this result involves system analytic arguments along with the Hartman–Grobman theorem. Using the notions of stability of sets, lower semicontinuous Lyapunov functions are constructed to provide a Lyapunov function proof of Poincar...

Input-to-State Stability (ISS) and the ISSLyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov func...

In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...