Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law 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.     

Periodic maintenance and repair rate control in stochastic manufacturing systems

In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.Research of this author was supported in part by the University of Georgia.Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.     

Control of Stochastic Systems with Time-Varying Multiple Time Delays: LMI Approach

This paper deals with the class of continuous-time linear systems with Markovian jumps and multiple time delays. The systems that we are treating are assumed to have time-varying delays in their dynamics which can be different and also have uncertainties in the system parameters. The time-varying structure of the bounded uncertainties is considered. Delay-dependent conditions for stochastic stability and stochastic stabilizability and their robustness are considered. A design algorithm for a stabilizing memoryless controller is proposed. All the results are given in the LMI formalism.     

Stabilization of stochastic singular nonlinear hybrid systems

This paper deals with the control of the class of singular nonlinear stochastic hybrid systems. Under some appropriate assumptions, results on stochastic stability and stochastic stabilization are developed. Two state feedback controllers (linear and nonlinear) that stochastically stabilize the class of systems we are considering are designed. LMI sufficient conditions are developed to compute the gains of these controllers.     

Dynamical Systems with Multiple Time-Varying Delays: Stability and Stabilizability

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. System robustness is also studied when the norm-bounded uncertainties are considered. LMI delay-dependent sufficient conditions for stability, stabilizability, and system robustness are established to check whether a system of this class is stable and/or stabilizable. Numerical examples are provided to show the usefulness of the proposed results.     

On Stability and Stabilizability of Singular Stochastic Systems with Delays

This paper deals with the class of continuous-time singular linear systems with Markovian jump parameters and time delays. Sufficient conditions on the stochastic stability and stochastic stabilizability are developed. A design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse free, and stochastically stable is proposed in terms of the solutions to linear matrix inequalities. The research of this author was supported by NSERC Grant RGPIN36444-02. The research of this author was supported by the Program for a New Century of Excellent Talents in the Universities and by the Foundation for the Authors of National Excellent Doctoral Dissertations of P. R. China, Grant 200240. The research of this author was supported by HKU Grant RGC 7029/05P.     

Robust$${\cal {H}}_{\infty}$$ Stabilization of Stochastic Hybrid Systems with Wiener Process

This paper deals with the class of uncertain continuous-time linear stochastic hybrid systems with Wiener process. The uncertainties that we are considering are of the norm-bounded type. The robust stochastic stabilization problem is treated. LMIs based sufficient conditions are developed to design the state feedback controller that robustly and stochastically stabilizes the studied class of systems and at the same time rejects a disturbance of desired level. The minimum disturbance rejection is also determined. A numerical example is provided to show the validity of the proposed results.     

Guaranteed Cost Control of a Markov Jump Linear Uncertain System Using a Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense.     

Stochastic Output Feedback of Uncertain Time-Delay Systems with Saturating Actuators

This paper deals with the class of uncertain continuous-time linear systems with Markovian jumps, time delay, and saturating actuators. Under norm-bounded uncertainties and based on the Lyapunov method, sufficient conditions on stochastic stability and stochastic stabilizability are developed. A design algorithm for a stabilizing observer-based robust output feedback controller is proposed in terms of the solutions of linear matrix inequalities.     

Stabilization of Singular Markovian Jump Systems with Discontinuities and Saturating Inputs

The problem of the stability and stabilization of Markov jumping singular systems with discontinuities and saturating inputs is addressed. The design procedure via linear matrix inequality technique (LMI) and the sequential linear programming matrix method (SLPMM) are used to determine simultaneously a state feedback control and an associated domain of safe admissible states for which the regularity, the absence of impulsive behavior and the stochastic stability in the mean square sense of the closed-loop systems are guaranteed. A numerical example is provided to demonstrate the effectiveness of the proposed methods.