Stabilization of continuous-time jump linear systems

• Published in: IEEE transactions on automatic control Vol. 47; no. 10; pp. 1590 - 1603
• Main Authors: Fang, Yuguang, Loparo, K.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-10-2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Asymptotic stability; Automatic control; Communication system control; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Controllability; Exact sciences and technology; Linear systems; Markov processes; Riccati equation; Riccati equations; Stability analysis; Stabilization; Stochastic processes; Stochasticity; Sufficient conditions; Markov process; Stabilizability; Linear system; Probabilistic approach; Stabilization; Controllability; Continuous time; Linear time; Jump process; Riccati equation
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.803528

We investigate almost-sure and moment stabilization of continuous time jump linear systems with a finite-state Markov jump form process. We first clarify the concepts of /spl delta/-moment stabilizability, exponential /spl delta/-moment stabilizability, and stochastic /spl delta/-moment stabilizability. We then present results on the relationships among these concepts. Coupled Riccati equations that provide necessary and sufficient conditions for mean-square stabilization are given in detail, and an algorithm for solving the coupled Riccati equations is proposed. Moreover, we show that individual mode controllability implies almost-sure stabilizability, which is not true for other types of stabilizability. Finally, we present some testable sufficient conditions for /spl delta/-moment stabilizability and almost-sure stabilizability.