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This paper deals with the exponential stabilization problem of discrete-time Markovian jump systems via a hybrid control strategy, in which the transition probability matrix and static output-feedback controller are designed simultaneously. A necessary and sufficient condition for the existence of an exponential stabilizing transition probability matrix is derived by means of a mode-dependent parametric approach. Furthermore, a sufficient condition is established for the above-mentioned hybrid design with a specified lower bound on the decay rate. The proposed design approaches can be applied to solve two kinds of control design problems with practical constraints imposed on the hybrid design. Besides, an estimation approach is proposed on the decay rate and decay coefficient of the jump systems. Also, two optimization problems are formulated to obtain the hybrid control strategy. Finally, two numerical examples and a network-on-chip based application are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming. [ABSTRACT FROM PUBLISHER]