A New Finite-Time Bounded Control of Stochastic Itô Systems with (x,u,v)-Dependent Noise: Different Quadratic Function Approach

Abstract

This paper addresses the finite-time bounded control problem of linear stochastic systems with state, control input, and external disturbance-dependent noise (($x,u,v$)-dependent noise for short). The notion of finite-time boundedness of linear stochastic systems is first introduced. Then a different quadratic function approach is proposed to give a sufficient condition for finite-time boundedness of such a class of systems, and its superiority to common quadratic approach is shown. Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. Finally, an example is employed to illustrate the effectiveness of our obtained results.