This paper studies the problem of H∞-control for linear systems with Markovian jumping parameters The jumping parameters considered here are two separable continuous-time, discrete-state Markov processes, one appearing in the system matrices and one appearing in the control variable Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed H∞-performance are achieved We also deal with the robust H∞-control problem for linear systems with both Markovian jumping parameters and parameter uncertainties The parameter uncertainties are assumed to be real, time-varying, norm-bounded, appearing in the state matrix Both the finite-horizon and infinite-horizon cases are analyzed We show that the control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of coupled differential Riccati equations for the finite-horizon case or algebraic Riccati equations for the infinite-horizon case Particularly, robust H∞-controllers are also designed when the jumping rates have parameter uncertainties

H ∞ -control for Markovian jumping linear systems with parametric uncertainty

The matrix sign function and computations in systems

We consider the time-optimal control of a dynamic system with jump parameters. The motivating example is that of a parts-manufacturing system in which machines fail and are reputed according to known Markov processes. It is desired to obtain a feedback control of parts-routing to machines, which minimizes the expected completion time of a given production target. Using a Dynamic Programming approach, we derive optimality conditions. These are used for solution of a simple example. It is seen that closed form solutions would be very hard to obtain for large problems, so alternative approaches are also discussed.

Time-optimal control of parts-routing in a manufacturing system with failure-prone machines

The problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime
systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique. Copyright

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

In this paper we construct a sequence of Lyapunov algebraic equations,whose solutions converge to the solutions of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems. The obtained solutions are positive semidefinite, stabilizing, and unique. The proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced-order decoupled Lyapunov equations, Several examples are included to demonstrate the procedure. >

Lyapunov iterations for optimal control of jump linear systems at steady state

A computational algorithm for solving a system of coupled matrix algebraic equations is presented in this paper. Such equations arise in optimal control problems of linear systems with jump parameters.

V. Gourishankar

Papers

A Computational Algorithm for Solving a System of Coupled Algebraic Matrix Riccati Equations