We investigate the finite-time boundary stabilization of a 1-D first order quasilinear hyperbolic system of diagonal form on [0,1]. The dynamics of both boundary controls are governed by a finite-time stable ODE. The solutions of the closed-loop system issuing from small initial data in Lip([0,1]) are shown to exist for all times and to reach the null equilibrium state in finite time. When only...

This paper addresses the problem of finite-time H∞ control via observer-based state feedback for a family of singular Markovian jump systems SMJSs with time-varying norm-bounded disturbance. Firstly, the concepts of singular stochastic finite-time boundedness and singular stochastic finite-time H∞ stabilization via observer-based state feedback are given. Then an observer-based state feedback c...

A causal feedback map, taking sequences of measurements and producing sequences of controls, is denoted as finite set if, within any finite time horizon, its range is in a finite set. Bit-rate constrained or digital control are particular cases of finite-set feedback. In this paper, we show that the finite gain (FG) lp stabilization, with 1 p ∞, of a discrete-time, linear and time-invariant uns...