http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/data/papers/2395.pdf

Brief paper: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.

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Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities

This paper focuses on the problem of neural-network-based decentralized adaptive output-feedback control for a class of nonlinear strict-feedback large-scale stochastic systems. The dynamic surface control technique is used to avoid the explosion of computational complexity in the backstepping design process. A novel direct adaptive neural network approximation method is proposed to approximate the unknown and desired control input signals instead of the unknown nonlinear functions. It is shown that the designed controller can guarantee all the signals in the closed-loop system to be semiglobally uniformly ultimately bounded in a mean square. Simulation results are provided to demonstrate the effectiveness of the developed control design approach.

Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems

Stability analysis for stochastic hybrid systems

Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.

Mehmet Karan

Papers

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities

Transition rate bounds for the stability robustness of continuous-time markovian jump linear systems