In this chapter, the problem of integrated fault detection, isolation, and control (IFDIC) design of continuous-time Markovian jump linear systems with uncertain transition probabilities and subject to both energy bounded and peak bounded disturbances is introduced and addressed. A single Markovian jump module designated as the IFDIC under a mixed robust H∞/H_/L1 framework is considered to simultaneously achieve the desired detection, isolation, and control objectives. Conventional mixed robust H∞/H_/L1 approaches to the fault detection and isolation (FDI) problem lead to conservative results due to the selection of identical Lyapunov matrices.

Chapter Contents:

• 4.1 Introduction
• 4.2 System description and problem formulation
• 4.2.1 System description
• 4.2.2 The IFDIC design problem formulation
• 4.3 Main results
• 4.4 Case study
• 4.5 Conclusion

Inspec keywords: H∞ control; Lyapunov matrix equations; stochastic systems; probability; fault diagnosis; robust control; linear systems; continuous time systems; control system synthesis

Other keywords: peak bounded disturbances; integrated fault detection, isolation, and control design; single Markovian jump module; identical Lyapunov matrices; continuous-time Markovian jump linear systems; IFDIC design; mixed robust H_∞-H_-L1 framework; uncertain transition probabilities; energy bounded disturbances

Subjects: Linear control systems; Optimal control; Control system analysis and synthesis methods; Other topics in statistics; Stability in control theory; Algebra; Time-varying control systems