Shifting finite time stability and boundedness design for continuous-time LPV systems

In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. In particular, the concepts of finite time stability (FTS) and finite time boundedness (FTB) are extended, introducing their shifting counterparts. By introducing new scheduling parameters, the controller can be designed in such a way that different values of these parameters imply different characteristics of the finite time stability/boundedness property. In this way, the performance of the control system can be varied during its operation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be also applied to LTI systems. The design conditions are feasibility problems involving linear matrix inequalities (LMIs) that can be solved efficiently using available solvers. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (author's final draft

Stochastic H ∞ Finite-Time Control of Discrete-Time Systems with Packet Loss

This paper investigates the stochastic finite-time stabilization and H ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic H ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic H ∞ finitetime stabilization of the class of stochastic systems. The stochastic H ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme

Stochastic ℋ

This paper investigates the stochastic finite-time stabilization and ℋ∞ control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochastic ℋ∞ finite-time boundedness and then state feedback controllers are designed to guarantee stochastic ℋ∞ finite-time stabilization of the class of stochastic systems. The stochastic ℋ∞ finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme