Smooth control with flexible duration for semi-Markov jump linear systems

Abstract

This paper is concerned with the issue of smooth control for semi-Markov jump linear systems. The performance metric on the control smoothness for general non-deterministic switched systems is renewed for the studied stochastic switched system by exploiting the statistical information including transition probabilities and sojourn-time probability mass functions. The practical asynchronous switching phenomenon in the system is considered. A piecewise control law with flexible transition-dependent duration for control smoothness is proposed as a first attempt, which outperforms the traditional fixed duration that is either less- or over-designed in terms of smoothness. A receding algorithm is developed to eliminate the nonlinearity curse caused by the terms of power of matrices in the derived existence criterion of controller. Illustrative examples including a class of hybrid terrestrial/aerial bicopters are presented to demonstrate the validity and applicability of the theoretical findings