Title :
On Stability and LQ Control of MJLS With a Markov Chain With General State Space
Author :
Kordonis, Ioannis ; Papavassilopoulos, George P.
Author_Institution :
Sch. of Electr. & Comput. Eng., Nat. Tech. Univ. of Athens, Athens, Greece
Abstract :
We study the mean square stability and the LQ control of discrete time Markov Jump Linear Systems where the Markov chain has a general state space. The mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector. Two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a Lyapunov equation and a uniformity result respectively. An algorithm for testing the mean square stability is also developed based on the uniformity result. The finite and infinite horizon LQ problems are considered and their solutions are characterized by appropriate Riccati integral equations. An application to Networked Control Systems (NCS) is finally presented and a simple example is studied via simulation.
Keywords :
Lyapunov methods; Markov processes; Riccati equations; discrete time systems; integral equations; linear quadratic control; linear systems; networked control systems; stability; state-space methods; LQ control; Lyapunov equation; Markov chain; NCS; Riccati integral equations; discrete time Markov jump linear systems; finite horizon LQ problems; infinite horizon LQ problems; mean square stability testing; networked control systems; simulation; spectral radius; state vector; Aerospace electronics; Delays; Equations; Markov processes; Mathematical model; Stability criteria; Markov jump linear systems; stochastic optimal control; stochastic stability;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2013.2274688
