Copositive Lyapunov Function Approach Research Articles

Protocol-Based Control for Discrete-Time Positive Markovian Switching Models With Deception Attacks

This brief investigates the problem of protocol-based control for positive Markovian switching models subject to actuator faults and deception attacks. Bernoulli distribution is adopted to depict random deception attacks. Considering the positivity of Markovian switching models, an event-triggered protocol is constructed based on a 1-norm to be related to the error signal and the state signal. In order to handle actuator faults and random cyber attacks, exponentially stochastic stability conditions are established under the event-triggered protocol by developing a linear copositive Lyapunov function approach. Furthermore, a non-fragile control law combined with the event-triggered protocol is proposed such that exponential stochastic stability of the corresponding system is achieved on the basis of matrix decomposition strategy and linear programming. Finally, a data communication network model is provided to demonstrate the effectiveness of the proposed controller design.

Finite-time contractive boundedness analysis and controller synthesis for interval positive linear systems under [formula omitted]-gain performance

This paper investigates the finite-time contractive boundedness (FTCB) analysis and controller synthesis problems for interval positive linear systems under L1-gain performance. Firstly, both FTCB and L1-gain FTCB definitions are extended to positive systems with disturbances. Subsequently, FTCB and L1-gain FTCB criteria are established for the considered positive systems by using the linear copositive Lyapunov function approach. Furthermore, the state feedback controller is designed to guarantee the positivity and L1-gain FTCB of the resulting closed-loop systems, and a convex optimization-based algorithm is given to derive the optimal L1-gain and controller parameter. Finally, a numerical example and an application example about pest control are used to verify the effectiveness of the proposed conditions.

Finite-time [formula omitted] and [formula omitted] boundedness for nonlinear singular switched positive systems with D-perturbations

The article studies the positivity, finite-time L1 boundedness and finite-time L∞ boundedness for nonlinear singular switched positive systems(NSSPSs) with D-perturbations. Firstly, a necessary and sufficient positivity condition is presented for NSSPSs by singular value decomposition approach. Then, considering the disturbance signal in the form of norm bounded integrable signal, based on average dwell time and co-positive Lyapunov function approach, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L1-gain performance, the result of finite-time L1 boundedness is presented for the considered system. In addition, considering the disturbance signal in the form of uniformly bounded signal, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L∞-gain performance, the result of finite-time L∞ boundedness is presented for the considered system. Finally, the correctness and effectiveness of the results are verified with four given examples.

Finite Time Annular Domain Robust Stability Analysis and Controller Design for T-S Fuzzy Interval Positive Systems

This paper is concerned with the finite time annular domain robust stability (FTADRS) analysis and controller design for T-S fuzzy positive systems with interval uncertainties. The concept of finite time annular domain stability is first introduced for positive systems. Based on this and using the copositive Lyapunov function approach, some sufficient conditions for FTADRS are derived. Subsequently, the finite time annular domain robust controller is designed via the linear programming technique. Finally, two numerical examples and an application example are employed to show the effectiveness of our results.

Dissipativity analysis and synthesis for positive Roesser systems under the switched mechanism and Takagi-Sugeno fuzzy rules

This paper addresses the dissipativity analysis and controller design for a class of T-S fuzzy positive systems which are described by the Roesser model. First, sufficient conditions obtained by utilizing the minimum dwell time method and co-positive Lyapunov function approach are given to guarantee the considered system is 2-D (ζ,η)-α-dissipative. Then via the state feedback fuzzy controller and the static output feedback fuzzy controller, criteria are also presented under which the resulting closed-loop systems are positive and 2-D (ζ,η)-α-dissipative. Moreover, the explicit design schemes for the desired controller parameters are also presented in the form of linear programming. Finally, a simple illustrative example is provided to show the validity of the approach outlined in this article.

New Results on Stability Analysis and Estimator Design for Switched Positive Linear Systems: A Reverse-Timer-Dependent Linear Co-Positive Lyapunov Function Approach

In this brief, the stability and estimator design issues are addressed for switched positive linear systems (SPLSs) with average dwell time (ADT). Based on a reverse timer which starts timing at the end of the activated time of a subsystem, a reverse-timer-dependent linear co-positive Lyapunov function (RLCLF) is constructed. With the help of the RLCLF approach, a new stability criteria is derived. Then, based on the stability criteria, a sufficient condition checking the existence of state estimator is derived for SPLSs with ADT. All the results can be relaxed into sum of square (SOS) program by using a SOS approximation approach. It's shown that the results obtained by RLCLF approach are less conservative compared with those of the literature. Finally, the advantages of the results are illustrated within two examples.

L1 filtering for continuous-discrete T-S fuzzy positive Roesser model

This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l1-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.

Reachable set estimation for switched positive systems

ABSTRACTThis paper focuses on the problem of reachable set estimation for discrete-time switched positive systems under two possible classes of exogenous disturbance. The multiple linear copositive Lyapunov function approach is applied to determine the bounding hyper-pyramids for the reachable set. Based on some Lyapunov-based inequalities and the linear version of the S-procedure technique, the bounding hyper-pyramids for the reachable set can be determined by solving a set of inequalities. Two optimisation methods are adopted to make the bounding hyper-pyramids as small as possible. Genetic Algorithm (GA) is utilised to search for the optimal value of the decision variables in the obtained inequalities. Finally, numerical examples are given to illustrate the effectiveness of the theoretical findings.

Mean Stability of Positive Markov Jump Linear Systems With Homogeneous and Switching Transition Probabilities

This brief investigates the mean stability problem of positive Markov jump linear systems (PMJLSs) in the discrete- time domain. First, some sufficient and necessary conditions are presented for PMJLSs with homogeneous transition probability (TP) by analyzing the time evolution of the first-order moment of the state. Then, by using a copositive Lyapunov function approach, a computable sufficient condition for the PMJLSs with switching TPs is proposed in the framework of dwell time to guarantee the mean stability. Finally, some numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

Robust model predictive control with ℓ1-gain performance for positive systems

This paper is concerned with robust model predictive control for positive systems. The technique of model predictive control is extended to the context of positive systems. By using the linear copositive Lyapunov function approach, a robust model predictive controller for positive systems is first constructed. Being unlike the classic robust control with ℓ2-gain performance, the robustness of the underlying systems is guaranteed by means of ℓ1-gain performance. In order to increase the feasibility of the present conditions, a multi-step control strategy is then utilized. Accordingly, a cone invariant set is addressed to satisfy the recursive feasibility of the present design. All present conditions can be described by linear programming. Meanwhile, the main computation of these conditions is completely off-line, by which the computational burden is reduced. Finally, an illustrative example is given to show the effectiveness of the design.

Robust finite‐time stability and stabilisation of switched positive systems

This study is concerned with robust finite-time stability and stabilisation of a class of switched positive systems. By using the multiple linear copositive Lyapunov function approach, sufficient conditions of finite-time stability and finite-time boundedness are constructed, respectively. l 1-gain is used to analyse the disturbance attenuation performance of the systems, and a finite-time weighted l 1-gain is obtained under bounded exogenous disturbances. Then, the problem of robust finite-time stabilisation of non-autonomous systems with a weighted l 1-gain is solved. All the proposed conditions are formulated in linear programming. Finally, two illustrative examples are given to show the validity of the theoretical results.