This paper is concerned with the issues of stability analysis and control synthesis for a class of discretetime semi-Markov jump linear systems (S-MJLSs). Motivated by the fact that the statistic characteristics of sojourn time and mode transitions are often difficult to acquire in practice, the sojourn-time probability density functions (ST-PDFs) and the transition probabilities (TPs) for jump instants are considered to be partially accessed. The systems under consideration is more general, which not only relaxes the conventional hypothesis on S-MJLSs that all the ST-PDFs and TPs are completely known but also covers systems with completely known and completely unknown ST-PDFs or TPs as special cases. By introducing the upper bound of sojourn time for each system mode, numerically testable stability criteria are established for S-MJLSs with incompletely available ST-PDFs and/or TPs in the sense of meansquare stability, and the existence conditions of desired stabilizing controller are developed to guarantee the mean-square stability of closed-loop S-MJLSs. The theoretical results are testified by several numerical examples and a practical example of space robot manipulator, to demonstrate the effectiveness, superiority and applicability of the developed control methodology.

This technical note is concerned with the problem of simultaneous design of observers and controllers for a class of piecewise-affine systems against signal quantization occurring in both measurement output and control input channels. The general scenario is considered that system state and estimated state may not be in the same operating region. By a novel quantization-errordependent Lyapunov function, the stability and H _∞ performance criteria are first established for the augmented system composed of a closed-loop control system and an estimation error system with the aid of S-procedure involving the region partition information of the original system. Then, by the cone complementary linearization algorithm, the desired observer and controller gains are solved simultaneously such that the resulting closed-loop system is asymptotically stable with a prescribed H _∞ performance index. Finally, a networked single-link robot arm is utilized to demonstrate the effectiveness of the proposed control strategy.

This technical note addresses the problem of simultaneous design of observer and controller for discrete-time nonhomogeneous semi-Markov jump linear systems (S-MJLSs) against mode mismatches between system and observer-based controller. The considered systems are more general than homogeneous S-MJLSs, and the mode mismatches are caused by time delays of mode switchings of controller. Based on the semi-Markov kernel approach, together with the Lyapunov function depending upon not only both the system and controller modes but also the time that has elapsed in the current mode, sufficient conditions on the existence of the desired mode-dependent observer-based controller are presented such that the augmented nonhomogeneous S-MJLS composed of a closed-loop control system and an estimation error system is sigma-error mean square stable. Finally, a practical example of a quarter-car active suspension is provided to validate the superiorities of the proposed control strategy.

This article investigates the stochastic stability analysis and stabilization problems for discrete-time Takagi–Sugeno fuzzy semi-Markov jump systems with upper-bounded sojourn time. The fuzzy rules can be different for different system modes. Consequently, the membership functions for fuzzy rules are dependent on the system modes. Allowing for the fact that semi-Markov kernel (SMK) are difficult to fully obtain in practice, the elements in the SMK of the underlying systems are deemed to be partly known, which is more general than both semi-Markov jump systems with completely available SMK and Markov jump systems with unknown transition probabilities. Afterward, the stability and stabilization conditions are established by part of the known SMK information and then by all the known SMK information. In the end, the validity and the superiority of our proposed theoretical results are exemplified via a single-link robot arm and a truck-trailer model.

This article investigates the state estimation issue of discrete-time Takagi-Sugeno fuzzy Markov jump affine systems that cover both traditional fuzzy Markov jump systems and fuzzy affine systems as two special cases. The original system is transformed into a Markov jump piecewise-affine system that varies with different operating regions. The fuzzy rules are dependent on the system mode, and accordingly, the partition of the state space is mode dependent. To analyze the stochastic stability of the estimation error system, a novel mode-dependent piecewise Lyapunov function is constructed, in which the region indices of both the plant state and the estimator state are mode dependent. Then, the existence for a simultaneously mode-dependent and region-dependent fuzzy affine estimator is investigated by virtue of the S-procedure and ellipsoidal outer approximation such that the estimation error system is stochastically stable with a prescribed H∞ performance. In the end, an illustrative example of a tunnel diode circuit is adopted to showcase the effectiveness and practicability of the developed state estimation strategy.