Showing papers by "Peng Shi published in 1999"

Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay

Abstract: This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution.

Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters

Abstract: Studies the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in the state and measurement equations. Stochastic quadratic stability of the above system is analyzed. A state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties, which is in terms of solutions of two sets of coupled algebraic Riccati equations.

On stabilization of uncertain linear systems with jump parameters

Abstract: In this paper, we study the problem of robust stabilizability of the class of uncertain linear systems with Markovian jumping parameters. Under the assumption of complete access to the continuous state, the stochastic stabilizability of the nominal system and the boundedness of the system's uncertainties, sufficient conditions which guarantee the robust stability of the uncertain systems are presented, which are in terms of a set of coupled algebraic Riccati equations. A numerical example is given to illustrate the potential of the proposed technique.

Robust H/sub /spl infin// control for linear discrete-time systems with norm-bounded nonlinear uncertainties

Abstract: This paper studies the problem of robust control of a class of uncertain discrete-time systems. The class of uncertain systems is described by a state-space model with linear nominal parts and norm-bounded nonlinear uncertainties in the state and output equations. The authors address the problem of robust H/sub /spl infin// control in which both robust stability and a prescribed H/sub /spl infin// performance are required to be achieved, irrespective of the uncertainties. It has been shown that instead of the nonlinear uncertain system, one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed, which is in terms of a Riccati inequality.

Robust control for Markovian jumping discrete-time systems

Abstract: In this paper, we investigate the H control problem for a class of linear discrete-time systems with Markovian jumping parameters. The jumping parameters considered here is modelled by adiscrete-time Markov process. Ourattentionisfocused onthedesign of linear state feedback controller such that both stochastic stability and a prescribed H performance are required to be achieved when the real system under consideration has different types of uncertainty. Sufficient conditions are proposed to solve the above problem, which are in terms of a set of solutions of coupled algebraic Riccati inequalities. An example is given to show the potential of the proposed techniques.

Guaranteed cost control of uncertain discrete-time systems with delay in state

Abstract: This paper considers the problems of robust guaranteed cost control of linear discrete timedelay systems with parametric uncertainties. By linear matrix inequality (LMI) approach, the robust quadratic stability of the system is studied. A control design method is developed such that the closed-loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays. Furthermore, the upper bound (cost) can be optimized by incorporating with a minimization problem.

Controller design for bilinear systems with parametric uncertainties

Abstract: This paper studies the problem of robust control of a class of uncertain bilinear continuous-time systems. The class of uncertain systems is described by a state space model with time-varying norm-bounded parameter uncertainty in the state equation. We address the problem of robust H∞ control in which both robust stability and a prescribed H∞ performance are required to be achieved irrespective of the uncertainties. Both state feedback and output feedback controllers are designed. It has been shown that the above problems can be recast into H∞ syntheses for related bilinear systems without parameter uncertainty, which can be solved via a Riccati inequality approach. Two examples are given to show the potential of the proposed technique.

Robust inventory-production control problem with stochastic demand

Abstract: This paper deals with the inventory-production control problem where the produced items are supposed to be deteriorating with a rate that depends on the stochastic demand rate. The inventory-production control problem is formulated as a jump linear quadratic control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost control problem is also investigated. Copyright © 1999 John Wiley & Sons, Ltd.

Robust stochastic stabilization of discrete-time linear systems with Markovian jumping parameters

Abstract: In this paper, we study the problem of robust stabilization of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A sufficient condition guaranteeing the robust stability of the uncertain di crete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, which is in terms of a set of coupled discrete-time algebraic Riccati inequalities (IEqs). Finally, a numerical example is given to show the potential of the proposed technique.

On designing H/sub /spl infin// controller for a class of nonlinear Markovian jump systems with parametric uncertainties

Abstract: This paper studies the problem of stochastic stability and disturbance attenuation for a class of uncertain nonlinear continuous-time systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state control and external disturbance dependent. A sufficient condition is presented to solve the above problem. An H/sub /spl infin// controller is designed which is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.

Filtering for Interconnected Nonlinear Sampled-Data Systems With Parametric Uncertainties

Abstract: The problem of H∞ filtering for a class of interconnected nonlinear continuous-time systems sub ject to real time-varying parameter uncertainty with sampled-data measurements is considered. Linear filters are designed that would guarantee a prescribed H∞ performance in the continuous-time context, irrespective of the parameter uncertainty, nonlinear interactions, and unknown initial states. Both the cases of finite and infinite horizon filtering are investigated in terms of a set of differential Riccati equations with finite discrete jumps. Two examples are given to show the potential of the proposed technique.

Robust Kalman filtering for continuous-time Markovian jump uncertain systems

Abstract: This paper studies the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in the state and measurement equations. Stochastic quadratic stability of the above system is analyzed. A state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties, which is in terms of solutions of two sets of coupled algebraic Riccati equations.

Memoryless controller design on discrete-time Markovian jump systems with parametric uncertainty and unknown delay

Abstract: This paper studies the problem of control for discrete time-delay linear systems with Markovian jump parameters. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time-delay.